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A001657
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Fibonomial coefficients.
(Formerly M4568 N1945)
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5
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1, 8, 104, 1092, 12376, 136136, 1514513, 16776144, 186135312, 2063912136, 22890661872, 253854868176, 2815321003313, 31222272414424, 346260798314872, 3840089017377228, 42587248616222024, 472299787252290712, 5237885063192296801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 74.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (8,40,-60,-40,8,1).
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FORMULA
| ((5+n, 5)) (see A010048), or fibonomial(5+n, 5).
G.f.: 1/(1-8*x-40*x^2+60*x^3+40*x^4-8*x^5-x^6) = 1/((1-x-x^2)*(1+4*x-x^2)*(1-11*x-x^2)) (see Comments to A055870).
a(n)= 11*a(n-1)+a(n-2)+((-1)^n)*fibonomial(n+3, 3), n >= 2; a(0)=1, a(1)=8; fibonomial(n+3, 3)= A001655(n).
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MAPLE
| with(combinat) : a:=n-> 1/30*fibonacci(n)*fibonacci(n+1)*fibonacci(n+2)*fibonacci(n+3)*fibonacci(n+4): seq(a(n), n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
A001657:=-1/(z**2+11*z-1)/(z**2-4*z-1)/(z**2+z-1); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| f[n_]:=Fibonacci[n]*Fibonacci[n+1]*Fibonacci[n+2]*Fibonacci[n+3]*Fibonacci[n+4]; lst={}; Do[AppendTo[lst, f[n]/30], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 12 2010]
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CROSSREFS
| Cf. A010048, A001654 - A001658.
Sequence in context: A138430 A164760 A109774 * A106260 A112121 A141383
Adjacent sequences: A001654 A001655 A001656 * A001658 A001659 A001660
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 27 2000
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