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Search: id:A056565
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| A056565 |
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Fibonomial coefficients. |
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+0
6
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| 1, 21, 714, 19635, 582505, 16776144, 488605194, 14169550626, 411591708660, 11948265189630, 346934172869802, 10072785423545712, 292460526776698763, 8491396839675395415, 246543315138161480670, 7158243695757340957617
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OFFSET
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0,2
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FORMULA
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a(n)= A010048(n+7, 7)=: Fibonomial(n+7, 7).
G.f. 1/p(8, n) with p(8, n)= 1-21*x-273*x^2+1092*x^3+1820*x^4-1092*x^5-273*x^6+21*x^7+x^8 = (1+x-x^2)*(1-4*x-x^2)*(1+11*x-x^2)*(1-29*x-x^2) (n=8 row polynomial of signed Fibonomial triangle A055870; see this entry for Knuth and Riordan references.).
Recursion: a(n)=29*a(n-1)+a(n-2)+((-1)^n)*A001657(n), n >= 2, a(0)=1, a(1)=21.
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MAPLE
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with(combinat): a:=n->1/3120*fibonacci(n)*fibonacci(n+1)*fibonacci(n+2)*fibonacci(n+3)*fibonacci\ (n+4)*fibonacci(n+5)*fibonacci(n+6): seq(a(n), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
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CROSSREFS
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Cf. A010048, A000045, A001654-8, A001076, A049666 (signed), A049667.
Sequence in context: A020246 A006934 A100713 this_sequence A009167 A012479 A078791
Adjacent sequences: A056562 A056563 A056564 this_sequence A056566 A056567 A056568
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 10 2000
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