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A056565
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Fibonomial coefficients.
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5
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1, 21, 714, 19635, 582505, 16776144, 488605194, 14169550626, 411591708660, 11948265189630, 346934172869802, 10072785423545712, 292460526776698763, 8491396839675395415, 246543315138161480670, 7158243695757340957617
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (21,273,-1092,-1820,1092,273,-21,-1).
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FORMULA
| 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.).
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
| 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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MATHEMATICA
| f[n_]:= Fibonacci[n] *Fibonacci[n+1] *Fibonacci[n+2] *Fibonacci[n+3] *Fibonacci[n+4] *Fibonacci[n+5] *Fibonacci[n+6]; Table[f[n]/3120], {n, 30}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 12 2010]
(Times@@@Partition[Fibonacci[Range[30]], 7, 1])/3120 (* From Harvey P. Dale, Apr 10 2011 *)
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PROG
| (MAGMA) [ &*[Fibonacci(n+k): k in [0..6]]/3120: n in [1..16] ]; // Bruno Berselli, Apr 11 2011
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CROSSREFS
| Cf. A010048, A000045, A001654-8, A001076, A049666 (signed), A049667.
Sequence in context: A020246 A006934 A100713 * A187359 A009167 A012479
Adjacent sequences: A056562 A056563 A056564 * A056566 A056567 A056568
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 10 2000
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