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A052562 a(n) = 5^n * n!. 26
1, 5, 50, 750, 15000, 375000, 11250000, 393750000, 15750000000, 708750000000, 35437500000000, 1949062500000000, 116943750000000000, 7601343750000000000, 532094062500000000000, 39907054687500000000000 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A000142, A008548, A008546, A034325, A000165, A047055, A047056. a(n)= A051150(n+1, 0) (first column of triangle).

Sequence in context: A093146 A049393 A047054 * A113132 A088992 A320502

Adjacent sequences:  A052559 A052560 A052561 * A052563 A052564 A052565

KEYWORD

nonn,easy

AUTHOR

Joe Keane (jgk(AT)jgk.org)

EXTENSIONS

Name changed by Arkadiusz Wesolowski, Oct 04 2011

STATUS

approved

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Last modified June 16 14:56 EDT 2019. Contains 324152 sequences. (Running on oeis4.)