A005443 a(n) = n! * Fibonacci(n). (Formerly M2034)

0, 1, 2, 12, 72, 600, 5760, 65520, 846720, 12337920, 199584000, 3552595200, 68976230400, 1450895846400, 32866215782400, 797681364480000, 20650793619456000, 568032822669312000, 16543733655601152000, 508598164809326592000, 16458582085314969600000

Offset

0,3

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..416

P. R. J. Asveld & N. J. A. Sloane, Correspondence, 1987

P. R. J. Asveld, Fibonacci-like differential equations with a polynomial nonhomogeneous term, Fib. Quart. 27 (1989), 303-309.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 511

Formula

a(n) = A039948(n, 1).

E.g.f.: x/(1-x-x^2). - Geoffrey Critzer, Sep 01 2013

a(n) = n*a(n-1) + n*(n-1)*a(n-2). - G. C. Greubel, Nov 20 2022

Maple

ZL:=[S, {a = Atom, b = Atom, S = Prod(X, Sequence(Prod(X, b))), X = Sequence(b, card >= 1)}, labelled]: seq(combstruct[count](ZL, size=n), n=0..18); # Zerinvary Lajos, Mar 26 2008

Mathematica

Table[Fibonacci[n]*n!, {n, 0, 25}] (* Zerinvary Lajos, Jul 09 2009 *)

Prog

(PARI) a(n) = n!*fibonacci(n); \\ Michel Marcus, Oct 30 2015
(Magma) [Factorial(n)*Fibonacci(n): n in [0..30]]; // G. C. Greubel, Nov 20 2022
(SageMath) [fibonaccI9n)*factorial(n) for n in range(31)] # G. C. Greubel, Nov 20 2022

Crossrefs

Cf. A000045, A000142, A005442, A039948.

Sequence in context: A358064 A348767 A335786 * A362796 A002867 A235359

Adjacent sequences: A005440 A005441 A005442 * A005444 A005445 A005446

Keyword

nonn,easy

Author

Simon Plouffe

Extensions

More terms from James A. Sellers, Dec 24 1999

Status

approved