OFFSET
0,2
COMMENTS
A simple regular expression in a labeled universe.
For n >= 1 a(n) is the order of the wreath product of the symmetric group S_n and the Abelian group (C_5)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 504
Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
FORMULA
a(n) = A051150(n+1, 0) (first column of triangle).
E.g.f.: 1/(1-5*x).
a(n) = 5*n*a(n-1) with a(0)=1.
G.f.: 1/(1-5*x/(1-5*x/(1-10*x/(1-10*x/(1-15*x/(1-15*x/(1-20*x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012
G.f.: 1/Q(0), where Q(k) = 1 - 5*x*(2*k+1) - 25*x^2*(k+1)^2/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Sep 28 2013
a(n) = n!*A000351(n). - R. J. Mathar, Aug 21 2014
From Amiram Eldar, Jun 25 2020: (Start)
Sum_{n>=0} 1/a(n) = e^(1/5) (A092514).
Sum_{n>=0} (-1)^n/a(n) = e^(-1/5) (A092618). (End)
MAPLE
spec := [S, {S=Sequence(Union(Z, Z, Z, Z, Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
with(combstruct):A:=[N, {N=Cycle(Union(Z$5))}, labeled]: seq(count(A, size=n)/5, n=1..16); # Zerinvary Lajos, Dec 05 2007
MATHEMATICA
Table[5^n*n!, {n, 0, 20}] (* Wesley Ivan Hurt, Sep 28 2013 *)
PROG
(Magma)[5^n*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Oct 05 2011
(PARI) {a(n) = 5^n*n!}; \\ G. C. Greubel, May 05 2019
(Sage) [5^n*factorial(n) for n in (0..20)] # G. C. Greubel, May 05 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joe Keane (jgk(AT)jgk.org)
EXTENSIONS
Name changed by Arkadiusz Wesolowski, Oct 04 2011
STATUS
approved