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

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

Offset: 0

Author

Simon Plouffe

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000045, A000142, A005442, A039948.

Programs

Magma

[Factorial(n)*Fibonacci(n): n in [0..30]]; // 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 *)

PARI

a(n) = n!*fibonacci(n); \\ Michel Marcus, Oct 30 2015

SageMath

[fibonacci(n)*factorial(n) for n in range(31)] # G. C. Greubel, Nov 20 2022

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

Extensions

More terms from James Sellers, Dec 24 1999