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A056566
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Fibonomial coefficients.
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2
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1, 34, 1870, 83215, 3994320, 186135312, 8771626578, 411591708660, 19344810307020, 908637119420910, 42689423937884208, 2005443612183077232, 94214069697350815795, 4426039514623184676790, 207929935924379904006970
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
| a(n)= A010048(n+8, 8)=: Fibonomial(n+8, 8).
G.f. 1/p(9, n) with p(9, n)= 1-34*x-714*x^2+4641*x^3+12376*x^4- 12376*x^5-4641*x^6+714*x^7+34*x^8-x^9 = (1-x)*(1+3*x+x^2)*(1-7*x+x^2)* (1+18*x+x^2)*(1-47*x+x^2) (n=9 row polynomial of signed Fibonomial triangle A055870; see this entry for Knuth and Riordan references.).
Recursion: a(n)=47*a(n-1)-a(n-2)+((-1)^n)*A001658(n), n >= 2, a(0)=1, a(1)=34.
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MAPLE
| with(combinat):a:=n->1/65520*fibonacci(n)*fibonacci(n+1)*fibonacci(n+2)*fibonacci(n+3)*fibonacci(n+4)*fibonacci(n+5)*fibonacci(n+6)*fibonacci(n+7): seq(a(n), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
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MATHEMATICA
| f[n_]:=Fibonacci[n]*Fibonacci[n+1]*Fibonacci[n+2]*Fibonacci[n+3]*Fibonacci[n+4]*Fibonacci[n+5]*Fibonacci[n+6]*Fibonacci[n+7]; lst={}; Do[AppendTo[lst, f[n]/65520], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 12 2010]
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CROSSREFS
| Cf. A010048, A000045, A001654-8, A056565, A001906 (signed), A004187, A049660 (signed), A049668.
Sequence in context: A123790 A202297 A086881 * A187591 A160471 A138590
Adjacent sequences: A056563 A056564 A056565 * A056567 A056568 A056569
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 10 2000
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