DESCRIPTION TRANSITION METAL COMPLEX COMPOUNDS, OLEFIN OLIGOMERIZATION CATALYSTS INCLUDING THE COMPOUNDS, AND PROCESSES FOR PRODUCING OLEFIN OLIGOMERS USING THE CATALYSTS FIELD OF THE INVENTION The present invention relates to transition metal complex compounds, olefin oligomerization catalysts including the compounds, and processes of producing olefin oligomers with the catalysts. BACKGROUND OF THE INVENTION Industrial olefin oligomerization is most often catalyzed by organoaluminum compounds or transition metal compounds. The oligomerization of ethylene in particular gives a mixture of α-olefins. Of the α-olefins, 1-hexene has a high demand as a material for polyolefins, and high-selectivity processes for 1-hexene are desired. The only selective process that has been used in the industry is trimerization of ethylene using chromium compounds (Patent Document 1). This process affords approximately 8 kg of 1-hexene per 1 mmol chromium atom-hour under an ethylene pressure of 100 bar. However, it is preferred that a higher activity is achieved under a lower pressure so that the costs for pressure and catalyst in the production can be reduced. Further, very few techniques have been reported for the production of 1-hexene by trimerizing ethylene with transition metal compounds other than chromium compounds (Patent Documents 2 and 3, Non-Patent Documents 1 and 2). Patent Document 1: United States Patent No. 5856257 Patent Document 2: JP-A-2004-524959 Patent Document 3: WO 01/68572 Non-Patent Document 1: Journal of American Chemical Society, 2001, Vol. 123, pp. 7423-7424 Non-Patent Document 2: Journal of Organometallic Chemistry, 2004, Vol. 689, pp. 3641-3668 SUMMARY OF THE INVENTION The present invention has been made in view of the aforementioned problems in the art. It is therefore an object of the invention to provide novel transition metal complex compounds, olefin oligomerization catalysts of superior activity containing the compounds, and processes for producing olefin oligomers in the presence of the olefin oligomerization catalysts. The present inventors studied diligently to solve the problems in the art. They have then found that olefin oligomerization catalysts containing a transition metal complex compound with a specific structure show excellent activity and are suited for use in olefin oligomerization. In particular, the catalysts are capable of catalyzing the oligomerization of ethylene as a starting material to afford a trimer of ethylene, i.e., 1-hexene, with high selectivity. The present invention has been completed based on the findings. The present invention relates to the following [1] to [17] . [1] A transition metal complex compound [A] represented by Formula (I) below: [Chem. 1] (Formula Removed ) wherein R1 to R6 are the same or different from each other and are each a hydrogen atom, a halogen atom, a hydrocarbon group, a heterocyclic compound residue, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a sulfur-containing group, a phosphorus-containing group, a silicon-containing group, a germanium-containing group or a tin-containing group, two or more of R1 to R6 may be linked,to each other, and R1 may be linked to Z; M is a transition metal atom of Group 3 to Group 10 of the periodic table; n is a valence of M; X is a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a sulfur-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a phosphorus-containing group, a halogen-containing group, a heterocyclic compound residue, a silicon-containing group, a germanium-containing group or a tin-containing group, the atoms or groups indicated by X may be the same or different from each other, and the groups indicated by X may be linked to each other to form a ring; Y is an oxygen atom, a nitrogen atom, a phosphorus atom or a sulfur atom; Z is a hydrocarbon group or a heterocyclic compound residue that may have a substituent group, and the minimum number of bonds linking Y with N is in the range of 4 to 6; the bond between Y and Z may be a double bond or a triple bond, and the bond between Y and R1 may be a double bond or a triple bond; and the dotted lines each denote a coordination bond. [2] The transition metal complex compound [A] described in [1], wherein the minimum number of bonds linking Y with N in the transition metal complex compound of Formula (I) is 5 or 6. [3] The transition metal complex compound [A] described in [1], wherein Y, N and Z in the transition metal complex compound of Formula (I) form a structure represented by Formula (II) below: [Chem. 2] (Formula Removed )wherein Y is an oxygen atom, a nitrogen atom, a phosphorus atom or a sulfur atom; and R7 to R10 are the same or different from each other and are each a hydrogen atom, a halogen atom, a hydrocarbon group, a heterocyclic compound residue, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a sulfur-containing group, a phosphorus-containing group, a silicon-containing group, a germanium-containing group or a tin-containing group, and when R7 to R10 are hydrocarbon groups, R7 and R8 may be linked to each other to form a ring and R9 and R10 may be linked to each other to form a ring. [4] The transition metal complex compound [A] described in any one of [1] to [3] , wherein M in the transition metal complex compound of Formula (I) is a transition metal atom of Group 4 of the periodic table, and n is 4. [5] A transition metal complex compound [A] represented by Formula (I') below: [Chem. 3] (Formula Removed )wherein R1 to R6 and R1' are the same or different from each other and are each a hydrogen atom, a halogen atom, a hydrocarbon group, a heterocyclic compound residue, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a sulfur-containing group, a phosphorus-containing group, a silicon-containing group, a germanium-containing group or a tin-containing group, two or more of R1' and R1 to R6 may be linked to each other, and R1 may be linked to Z; M is a transition metal atom of Group 3 to Group 10 of the periodic table; n is a valence of M; X is a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a sulfur-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a phosphorus-containing group, a halogen-containing group, a heterocyclic compound residue, a silicon-containing group, a germanium-containing group or a tin-containing group, the atoms or groups indicated by X may be the same or different from each other, and the groups indicated by X may be linked to each other to form a ring; Y' is a nitrogen atom or a phosphorus atom; Z is a hydrocarbon group or a heterocyclic compound residue that may have a substituent group, and the minimum number of bonds linking Y' with N is in the range of 4 to 6; and the dotted lines each denote a coordination bond. [6] The transition metal complex compound [A] described in [5], wherein the minimum number of bonds linking Y' with N in the transition metal complex compound of Formula (I') is 5 or 6. [7] The transition metal complex compound [A] described in [5], wherein Y', N and Z in the transition metal complex compound of Formula (I' ) form a structure represented by Formula (II') below: [Chem. 4] (Formula Removed )wherein Y' is a nitrogen atom or a phosphorus atom; and R7 to R10 are the same or different from each other and are each a hydrogen atom, a halogen atom, a hydrocarbon group, a heterocyclic compound residue, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a sulfur-containing group, a phosphorus-containing group, a silicon-containing group, a germanium-containing group or a tin-containing group, and when R7 to R10 are hydrocarbon groups, R7 and R8 may be linked to each other to form a ring and R9 and R10 may be linked to each other to form a ring. [8] The transition metal complex compound [A] described in any one of [5] to [7] , wherein M in the transition metal complex compound of Formula (I') is a transition metal atom of Group 4 of the periodic table, and n is 4. [9] An olefin oligomerization catalyst comprising the transition metal complex compound [A] described in any one of [1] to [8] . [10] The olefin oligomerization catalyst described in [9] , wherein the catalyst comprises: [A] the transition metal complex compound; and [B] at least one compound selected from the group consisting of (b-1) an organometallic compound, (b-2) an organoaluminum oxγ-compound and (b-3) a compound which reacts with the transition metal complex compound [A] to form an ion pair. [11] The olefin oligomerization catalyst described in [9] , wherein the catalyst comprises: [A] the transition metal complex compound; [B] at least one compound selected from the group consisting of (b-1) an organometallic compound, (b-2) an organoaluminum oxγ-compound and (b-3) a compound which reacts with the transition metal complex compound [A] to form an ion pair; and [C] a carrier to support at least one compound selected from [A] and [B]. [12] A process for producing an olefin oligomer, comprising oligomerizing an olefin in the presence of the olefin oligomerization catalyst described in any one of [9] to [11] . [13] A process for producing an olefin oligomer, comprising oligomerizing an olefin in the presence of the olefin oligomerization catalyst described in any one of [9] to [11] and with a C5-7 linear saturated hydrocarbon as a solvent. [14] A process for producing an olefin oligomer, comprising oligomerizing an olefin in the presence of the olefin oligomerization catalyst described in any one of [9] to [11] and hydrogen. [15] A process for producing an olefin oligomer, comprising oligomerizing an olefin in the presence of the olefin oligomerization catalyst described in any one of [9] to [11] and an antistatic agent. [16] The process described in any one of [12] to [15], wherein the olefin is ethylene. [17] The process described in any one of [12] to [15], wherein the olefin is ethylene and the olefin oligomer is 1-hexene. ADVANTAGES OF THE INVENTION The transition metal complex compounds according to the present invention and the olefin oligomerization catalysts including the compounds have high activity. The processes for producing olefin oligomers according to the present invention use the olefin oligomerization catalysts. The processes enable the oligomerization of ethylene into 1-hexene with high activity and high selectivity, providing very high industrial values. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a 1H NMR spectrum of Compound 2. Fig. 2 is a 1H NMR spectrum of Compound 5. Fig. 3 is a 1H NMR spectrum of Compound 7. Fig. 4 is a 1H NMR spectrum of Compound 22. Fig. 5 is a 1H NMR spectrum of Compound 30. Fig. 6 is a 1H NMR spectrum of Compound 31. Fig. 7 is a 1H NMR spectrum of Compound 33. Fig. 8 is a 1H NMR spectrum of Compound 34. Fig. 9 is a 1H NMR spectrum of Compound 36. Fig. 10 is a 1H NMR spectrum of Compound 37. Fig. 11 is a 1H NMR spectrum of Compound 38. BEST MODE FOR CARRYING OUT THE INVENTION The transition metal complex compounds, the olefin oligomerization catalysts and the processes of producing olefin oligomers using the olefin oligomerization catalysts according to the present invention will be described in detail hereinbelow. In the invention, the olefin oligomerization refers to the production of dimers to decamers of olefins. An olefin oligomerization catalyst according to the invention includes a transition metal complex compound [A] described later. The olefin oligomerization catalyst usually contains, in addition to the transition metal complex compound [A] , at least one compound [B] selected from the group consisting of (b-1) an organometallic compound, (b-2) an organoaluminum oxγ-compound and (b-3) a compound which reacts with the transition metal complex compound [A] to form an ion pair. The compound (b-3) which reacts with the transition metal complex compound [A] to form an ion pair is also referred to as the ionizing ionic compound in the invention. The olefin oligomerization catalyst may contain a carrier [C] to support at least one compound selected from [A] and [B] . [Transition metal complex compounds [A]] The transition metal complex compounds [A] in the invention have two embodiments. The transition metal complex compounds in the first embodiment are represented by Formula (I) below: [Chem. 5] (Formula Removed ) In Formula (I), R1 to R6 are the same or different from each other and are each a hydrogen atom, a halogen atom, a hydrocarbon group, a heterocyclic compound residue, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a sulfur-containing group, a phosphorus-containing group, a silicon-containing group, a germanium-containing group or a tin-containing group. Two or more of R1 to R6 may be linked to each other, and R1 may be linked to Z. More specifically, R1 to R6 are each preferably a hydrogen atom, a halogen atom, a hydrocarbon group, a heterocyclic compound residue, a hydrocarbon-substituted silyl group, a hydrocarbon-substituted siloxy group, an alkoxy group, an alkylthio group, an aryloxy group, an arylthio group, an acyl group, an ester group, a thioester group, an amide group, an imide group, an amino group, an imino group, a sulfonate group, a sulfonamide group, a cyano group, a nitro group, a carboxyl group, a sulfo group, a mercapto group, an aluminum-containing group or a hydroxyl group. Examples of the halogen atoms include fluorine, chlorine, bromine and iodine. Examples of the hydrocarbon groups include linear or branched alkyl groups of 1 to 30, preferably 1 to 20, and more preferably 1 to 10 carbon atoms such as methyl, ethyl, n-propyl, isopropyl, n-butyl, isobutyl, sec-butyl, tert-butyl, neopentyl and n-hexyl; linear or branched alkenyl groups of 2 to 30, and preferably 2 to 20 carbon atoms such as vinyl, allyl and isopropenyl; linear or branched alkynyl groups of 2 to 30, and preferably 2 to 20 carbon atoms such as ethynyl and propargyl; cyclic saturated hydrocarbon groups of 3 to 30, and preferably 3 to 20 carbon atoms such as cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl and adamantyl; cyclic unsaturated hydrocarbon groups of 5 to 30 carbon atoms such as cyclopentadienyl, indenyl and fluorenyl; aryl groups of 6 to 30, and preferably 6 to 20 carbon atoms such as phenyl, naphthyl, biphenyl, terphenyl, phenanthryl and anthracenyl; alkyl-substituted aryl groups such as tolyl, isopropylphenyl, t-butylphenyl, dimethylphenyl and di-t-butylphenyl; and alkylidene groups of 1 to 30, and preferably 5 to 10 carbon atoms such as benzylidene, methylidene and ethylidene. The hydrocarbon groups may have hydrogen atoms substituted with halogens. Examples of such substituted groups include halogenated hydrocarbon groups of 1 to 30, and preferably 1 to 20 carbon atoms such as trifluoromethyl, pentafluorophenyl and chlorophenyl. The hydrocarbon groups may have hydrogen atoms substituted with other hydrocarbon groups. Examples of such groups include aryl-substituted alkyl groups such as benzyl, cumyl, diphenylethyl and trityl. The hydrocarbon groups may have heterocyclic compound residues; oxygen-containing groups such as alkoxy groups, aryloxy groups, ester groups, ether groups, acyl groups, carboxyl groups, carbonate groups, hydroxyl groups, peroxy groups and carboxylic anhydride groups; nitrogen-containing groups such as amino groups, imino groups, amide groups, imide groups, hydrazino groups, hydrazono groups, nitro groups, nitroso groups, cyano groups, isocyano groups, cyanate groups, amidino groups, diazo groups and amino groups in ammonium salt form; boron-containing groups such as boranediyl groups, boranetriyl groups and diboranyl groups; sulfur-containing groups such as mercapto groups, thioester groups, dithioester groups, alkylthio groups, arylthio groups, thioacyl groups, thioether groups, thiocyanate groups, isothiocyanate groups, sulfonate groups, sulfonamide groups, thiocarboxyl groups, dithiocarboxyl groups, sulfo groups, sulfonyl groups, sulfinyl groups and sulfenyl groups; phosphorus-containing groups such as phosphide groups, phosphoryl groups, thiophosphoryl groups and phosphate groups; silicon-containing groups; germanium-containing groups; and tin-containing groups. Of these, particularly preferred groups are linear or branched alkyl groups of 1 to 30, preferably 1 to 20, more preferably 1 to 10, and still more preferably 2 to 10 carbon atoms such as methyl, ethyl, n-propyl, isopropyl, n-butyl, isobutyl, sec-butyl, t-butyl, neopentyl, n-hexyl and adamantyl; aryl groups of 6 to 30, and preferably 6 to 20 carbon atoms such as phenyl, naphthyl, biphenyl, terphenyl, phenanthryl and anthracenyl; and substituted aryl groups wherein the above aryl groups are substituted with 1 to 5 substituent groups such as halogen atoms, alkyl or alkoxy groups of 1 to 30, and preferably 1 to 20 carbon atoms, and aryl or aryloxy groups of 6 to 30, and preferably 6 to 20 carbon atoms. Examples of the heterocyclic compound residues include residues of nitrogen-containing compounds such as pyrrole, pyridine, pyrimidine, quinoline and triazine; residues of oxygen-containing compounds such as furan and pyran; residues of sulfur-containing compounds such as thiophene; and groups obtained by substituting the above heterocyclic compound residues with substituent groups such as alkyl groups and alkoxy groups of 1 to 30, and preferably 1 to 20 carbon atoms. Examples of the oxygen-containing groups, the nitrogen-containing groups, the sulfur-containing groups and the phosphorus-containing groups include the groups mentioned above as substituent groups for the hydrocarbon groups. Examples of the boron-containing groups include the groups mentioned above as substituent groups for the hydrocarbon groups, and alkylboron groups, arylboron groups, boron halide groups and alkylboron halide groups. The alkylboron groups include (Et)2B-, (iPr)2B-, (iBu)2B-, (Et)3B, (iPr)3B and (iBu)3B. The arylboron groups include (C6H5)2B-, (C6H5)3B, (C6F5)3B and (3, 5-(CF3) 2C6H3) 3B. The boron halide groups include BC12- and BC13. The alkylboron halide groups include (Et)BCl-, (iBu)BCl-and (C6H5)2BC1. In the above groups, the trisubstituted boron is often coordination bonded. Here, Et denotes an ethyl group, iPr an isopropyl group, and iBu an isobutyl group. Examples of the aluminum-containing groups include alkylaluminum groups, arylaluminum groups, aluminum halide groups and alkylaluminum halide groups. The alkylaluminum groups include (Et)2Al-, (iPr)2Al-, (iBu)2Al-, (Et)3Al, (iPr)3Al and (iBu)3Al. The arylaluminum groups include (C6H5)2A1-. The aluminum halide groups include A1C12- and A1C13. The alkylaluminum halide groups include (Et)AlCl- and (iBu)AlCl-. In the above groups, the trisubstituted aluminum is often coordination bonded. Here, Et denotes an ethyl group, iPr an isopropyl group, and iBu an isobutyl group. Examples of the silicon-containing groups include silyl groups, siloxy groups, hydrocarbon-substituted silyl groups and hydrocarbon-substituted siloxy groups. The hydrocarbon-substituted silyl groups include methylsilyl, dimethylsilyl, trimethylsilyl, ethylsilyl, diethylsilyl, triethylsilyl, diphenylmethylsilyl, triphenylsilyl, dimethylphenylsilyl, dimethyl-t-butylsilyl and dimethyl(pentafluorophenyl)silyl. Of these, methylsilyl, dimethylsilyl, trimethylsilyl, ethylsilyl, diethylsilyl, triethylsilyl, dimethylphenylsilyl and triphenylsilyl are preferred, and trimethylsilyl, triethylsilyl, triphenylsilyl and dimethylphenylsilyl are particularly preferred. The hydrocarbon-substituted siloxy groups include trimethylsiloxy group. Examples of the germanium-containing groups and the tin-containing groups include groups corresponding to the above silicon-containing groups except that the silicon is replaced by germanium or tin. Of the nitrogen-containing groups, preferred amide groups include acetamide, N-methylacetamide and N-methylbenzamide; preferred amino groups include dimethylamino, ethylmethylamino and diphenylamino; preferred imide groups include acetimide and benzimide; and preferred imino groups include methylimino, ethylimino, propylimino, butylimino and phenylimino. Of the sulfur-containing groups, preferred alkylthio groups include methylthio and ethylthio; preferred arylthio groups include phenylthio, methylphenylthio and naphthylthio; preferred thioester groups include acetylthio, benzoylthio, methylthiocarbonyl and phenylthiocarbonyl; preferred sulfonate groups include methyl sulfonate, ethyl sulfonate and phenyl sulfonate; and preferred sulfonamide groups include phenylsulfonamide, N-methylsulfonamide and N-methyl-p-toluenesulfonamide. Two or more of R1 to R6 may be linked together. Preferably, adjacent groups of R1 to R6 are linked together to form an alicyclic ring, an aromatic ring, or a heterohydrocarbon ring containing heteroatoms such as nitrogen. These rings may have substituent groups. R1 may be linked to Z, in which case the linkage of R1 with Z may form an aromatic ring, an alicyclic ring, or a heterohydrocarbon ring containing heteroatoms such as nitrogen, and these rings may have substituent groups. R1 is preferably a methyl group, an ethyl group or an isopropyl group, and is particularly preferably a methyl group. R2 is preferably a phenyl group, an α-cumyl group, a tert-butyl group or a 1-adamantyl group, and is particularly preferably a 1-adamantyl group. R4 is preferably a methyl group, a cyclohexyl group, a tert-butyl group or a 1-adamantyl group, and is particularly preferably a methyl group. In Formula (I), M is a transition metal atom of Group 3 to Group 10 of the periodic table, and n is a valence of M. Preferred examples of M include yttrium, scandium, lanthanum, samarium, titanium, zirconium, hafnium, vanadium, tantalum, chromium, cobalt, iron, nickel and copper. M is more preferably a transition metal atom of Group 4 of the periodic table such as titanium, zirconium or hafnium, and is particularly preferably titanium. Particularly preferably, the letter n is 3 for yttrium, scandium and lanthanum, is 2 for samarium, is 4 for Group 4 transition metal atoms such as titanium, zirconium and hafnium, is 3 to 5 for vanadium and tantalum, is 3 for chromium, and is 2 for cobalt, iron, nickel and copper. In Formula (I), X is a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a sulfur-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a phosphorus-containing group, a halogen-containing group, a heterocyclic compound residue, a silicon-containing group, a germanium-containing group or a tin-containing group. The atoms or groups indicated by X may be the same or different from each other, and the groups indicated by X may be linked to each other to form a ring. Examples of the halogen atoms include fluorine, chlorine, bromine and iodine. Examples of the hydrocarbon groups include those mentioned for R1 to R6 in Formula (I) . Specific examples include, but are not limited to, alkyl groups such as methyl, ethyl, propyl, butyl, hexyl, octyl, nonyl, dodecyl and eicosyl; cycloalkyl groups of 3 to 30 carbon atoms such as cyclopentyl, cyclohexyl, norbornyl and adamantyl; alkenyl groups such as vinyl, propenyl and cyclohexenyl; arylalkyl groups such as benzyl, phenylethyl and phenylpropyl; and aryl groups such as phenyl, tolyl, dimethylphenyl, trimethylphenyl, ethylphenyl, propylphenyl, biphenyl, naphthyl, methylnaphthyl, anthryl and phenanthryl. Examples of the hydrocarbon groups further include halogenated hydrocarbon groups, specifically hydrocarbon groups of 1 to 30, and preferably 1 to 20 carbon atoms wherein at least one hydrogen is substituted with halogen. Examples of the heterocyclic compound residues include those mentioned for R1 to R6 in Formula (I). Examples of the oxygen-containing groups include those mentioned for R1 to R6 in Formula (I). Specific examples include, but are not limited to, hydroxyl group; alkoxy groups such as methoxy, ethoxy, propoxy and butoxy; aryloxy groups such as phenoxy, methylphenoxy, dimethylphenoxy and naphthoxy; arylalkoxy groups such as phenylmethoxy and phenylethoxy; acetoxy groups; and carbonyl groups. Examples of the sulfur-containing groups include those mentioned for R1 to R6 in Formula (I). Specif ic examples include, but are not limited to, sulfonate groups such as methyl sulfonate, trifluoromethane sulfonate, phenyl sulfonate, benzyl sulfonate, p-toluene sulfonate, trimethylbenzene sulfonate, triisobutylbenzene sulfonate, p-chlorobenzene sulfonate and pentafluorobenzene sulfonate; sulfinate groups such as methyl sulfinate, phenyl sulfinate, benzyl sulfinate, p-toluene sulfinate, trimethylbenzene sulfinate and pentafluorobenzene sulfinate; alkylthio groups; and arylthio groups. Examples of the nitrogen-containing groups include those mentioned for R1 to R6 in Formula (I) . Specific examples include, but are not limited to, amino groups; alkylamino groups such as methylamino, dimethylamino, diethylamino, dipropylamino, dibutylamino and dicyclohexylamino; and arylamino groups and alkylarylamino groups such as phenylamino, diphenylamino, ditolylamino, dinaphthylamino and methylphenylamino. Examples of the boron-containing groups include BR4 other than tetraphenyl borate (where R is a hydrogen atom, an alkyl group, an optionally substituted aryl group, or a halogen atom) . Examples of the phosphorus-containing groups include, but are not limited to, trialkylphosphine groups such as trimethylphosphine, tributylphosphine and tricyclohexylphosphine; triarylphosphine groups such as triphenylphosphine and tritolylphosphine; phosphite groups (phosphide groups) such as methyl phosphite, ethyl phosphite and phenyl phosphite; phosphonic acid groups; and phosphinic acid groups. Examples of the silicon-containing groups include those mentioned for R1 to R6 in Formula (I) . Specific examples include hydrocarbon-substituted silyl groups such as phenylsilyl, diphenylsilyl, trimethylsilyl, triethylsilyl, tripropylsilyl, tricyclohexylsilyl, triphenylsilyl, methyldiphenylsilyl, tritolylsilyl and trinaphthylsilyl; hydrocarbon-substituted silyl ether groups such as trimethylsilyl ether; silicon-substituted alkyl groups such as trimethylsilylmethyl; and silicon-substituted aryl groups such as trimethylsilylphenyl. Examples of the germanium-containing groups include those mentioned for R1 to R6 in Formula (I) . Specific examples include groups corresponding to the above silicon-containing groups except that the silicon is replaced by germanium. Examples of the tin-containing groups include those mentioned for R1 to R6 in Formula (I) . Specific examples include groups corresponding to the above silicon-containing groups except that the silicon is replaced by tin. Examples of the halogen-containing groups include, but are not limited to, fluorine-containing groups such as PF6 and BF4; chlorine-containing groups such as C104 and SbCl6; and iodine-containing groups such as IO4. Examples of the aluminum-containing groups include, but are not limited to, A1R4 (where R is a hydrogen atom, an alkyl group, an optionally substituted aryl group, or a halogen atom) . Of the above atoms and groups indicated by X, the halogen atoms and the alkyl groups are preferred, and chlorine, bromine and methyl are more preferred. In Formula (I), Y is an oxygen atom, a nitrogen atom, a phosphorus atom or a sulfur atom, and constitutes an ether structure, a ketone structure, an amine structure or an imine structure. In Formula (I) , Z is a hydrocarbon group or a heterocyclic compound residue that may have a substituent group, and the minimum number of bonds linking Y with N is in the range of 4 to 6. By limiting the minimum number of bonds linking Y with N in the range of 4 to 6, the olefin oligomerization catalyst containing the transition metal complex compound [A] catalyzes the oligomerization of ethylene to afford 1-hexene with high selectivity. Preferably, the minimum number of bonds linking Y with N is 5 or 6, in which case the selectivity for 1-hexene is further increased. If the minimum number of bonds between Y and N is 3 or less, the distance between Y and N is not sufficient and the catalyst works to polymerize ethylene, that is, the catalyst is an olefin polymerization catalyst similar to compounds described in WO 2001/44324, Organometallics, 2004, Vol. 23, pp. 1684-1688, and Organometallics, 2006, Vol. 25, pp. 3259-3266. Consequently, oligomers such as 1-hexene are not produced as expected. If the minimum number of bonds between Y and N is 7 or more, Y cannot be coordinated to the metal atom M, and the catalyst works to polymerize ethylene, that is, the catalyst is an olefin polymerization catalyst similar to compounds without Y as described in Dalton Transaction, 2005, pp. 561-571. Consequently, oligomers such as 1-hexene are not produced as expected. The minimum number of bonds linking Y with N is counted as shown in (A) and (B) below, in which the minimum numbers are 4 and 5, respectively. [Chem. 6] (Formula Removed )The letter Z denotes a group linking N and Y. Preferably, Y, N and Z form a structure represented by Formula (II): [Chem. 7] (Formula Removed ) wherein Y is an oxygen atom, a nitrogen atom, a phosphorus atom or a sulfur atom; and R7 to R10 are the same or different from each other and are each a hydrogen atom, a halogen atom, a hydrocarbon group, a heterocyclic compound residue, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a sulfur-containing group, a phosphorus-containing group, a silicon-containing group, a germanium-containing group or a tin-containing group, and when R7 to R10 are hydrocarbon groups, R7 and R8 may be linked to each other to form a ring and R9 and R10 may be linked to each other to form a ring. Specific examples of R7 to R10 include those described for R1 to R6 in Formula (I) . Specific examples of the structures formed by Y, N and Z include those represented by Formulae (C) to (H) below but are not limited thereto. In the structures of Formulae (C) to (H) , hydrogen atoms may be substituted with the groups mentioned above as substituent groups for R1 to R6. In some of the structures of Formulae (C) to (H), R1 is linked to Z. In the structures illustrated below, the wavy lines adjacent to a carbon-carbon double bond indicate a cis-isomer or a trans-isomer. Chem. 8] (Formula Removed )[Chem. 9] (Formula Removed ) [Chem. 10] (Formula Removed ) [Chem. 11] (Formula Removed ) Chem. 12] (Formula Removed ) [Chem. 13] (Formula Removed ) In Formula (I), the bond between Y and Z may be a double bond or a triple bond, and the bond between Y and R1 may be a double bond or a triple bond. In Formula (I), the dotted lines each denote a coordination bond. The transition metal complex compounds [A] in the second embodiment are represented by Formula (I') below: [Chem. 14] (Formula Removed ) In Formula (I' ) , R1 to R6 and R1' are the same or different from each other and are each a hydrogen atom, a halogen atom, a hydrocarbon group, a heterocyclic compound residue, an oxygen-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a sulfur-containing group, a phosphorus-containing group, a silicon-containing group, a germanium-containing group or a tin-containing group. Two or more of R1' and R1 to R6 may be linked to each other, and R1 may be linked to Z. Examples of R1 to R6 and R1' in Formula (I') include those mentioned for R1 to R6 in Formula (I). In Formula (I'), M is a transition metal atom of Group 3 to Group 10 of the periodic table, and n is a valence of M. Examples of M and n in Formula (I' ) include those mentioned for M and n in Formula (I) . In Formula {I) , X is a hydrogen atom, a halogen atom, a hydrocarbon group, an oxygen-containing group, a sulfur-containing group, a nitrogen-containing group, a boron-containing group, an aluminum-containing group, a phosphorus-containing group, a halogen-containing group, a heterocyclic compound residue, a silicon-containing group, a germanium-containing group or a tin-containing group. The atoms or groups indicated by X may be the same or different from each other, and the groups indicated by X may be linked to each other to form a ring. Examples of X in Formula (I' ) include those mentioned for X in Formula (I). In Formula (I' ) , Y' is a nitrogen atom or a phosphorus atom. In Formula (I' ) , Z is a hydrocarbon group or a heterocyclic compound residue that may have a substituent group, and the minimum number of bonds linking Y' with N is in the range of 4 to 6. By limiting the minimum number of bonds linking Y' with N in the range of 4 to 6, the olefin oligomerization catalyst containing the transition metal complex compound [A] catalyzes the oligomerization of ethylene to afford 1-hexene with high selectivity. Preferably, the minimum number of bonds linking Y' with N is 5 or 6, in which case the selectivity for 1-hexene is further increased. Specific examples of the structures formed by Y', N and Z include those represented by Formulae (I) to (K) below but are not limited thereto. In the structures of Formulae (I) to (K) , hydrogen atoms may be substituted with the groups mentioned above as substituent groups for R1 to R6 in Formula (I) . In some of the structures of Formulae (I) to (K) , R1 is linked to Z. In the structures illustrated below, the wavy lines adjacent to a carbon-carbon double bond indicate a cis-isomer or a trans-isomer. [Chem. 15] [Chem. 16] [Chem. 17] (Formula Removed ) In Formula (I'), the dotted lines each denote a coordination bond. The transition metal complex compounds [A] of Formula (I) and Formula (I') may be synthesized according to a method described in Journal of Organometallic Chemistry, 2003, Vol. 678, pp. 134-141. The reaction product by the method described in the above literature is a mixture but may be used directly as an olefin oligomerization catalyst without purification. Preferably, the product is used after purified by recrystallization or the like. In the invention, the transition metal complex compounds of Formula (I) and the transition metal complex compounds of Formula (I') may be collectively referred to as the transition metal complex compounds [A] . In addition to the transition metal complex compound [A] , the olefin oligomerization catalyst according to the present invention usually contains at least one compound [B] selected from the group consisting of (b-1) an organometallic compound, (b-2) an organoaluminum oxγ-compound and (b-3) a compound which reacts with the transition metal complex compound [A] to form an ion pair. The catalyst may further contain a carrier [C] to support at least one compound selected from [A] and [B]. Hereinbelow, the organometallic compounds (b-1), organoaluminum oxγ-compounds (b-2), and compounds (b-3) which react with the transition metal complex compound [A] to form an ion pair will be described. [Organometallic compounds (b-1)] Examples of the organometallic compounds (b-1) that are optionally used in the invention include organometallic compounds containing metals of Group 1, Group 2, Group 12 and Group 13 of the periodic table. Specific examples include compounds (b-la), (b-lb) and (b-lc) described below. In the invention, the organometallic compounds (b-1) do not include the organoaluminum oxγ-compounds (b-2). (b-la) Organoaluminum compounds represented by the following formula: (Formula Removed ) wherein R and R , which may be the same or dxfferent, are each a hydrocarbon group of 1 to 15, and preferably 1 to 4 carbon atoms; X is a halogen atom; 0