A051262 10-factorial numbers.

1, 10, 200, 6000, 240000, 12000000, 720000000, 50400000000, 4032000000000, 362880000000000, 36288000000000000, 3991680000000000000, 479001600000000000000, 62270208000000000000000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

For n >= 1 a(n) is the order of the wreath product of the symmetric group S_n and the Abelian group (C_10)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for sequences related to factorial numbers

Crossrefs

a(n) = A048176(n+1, 0)*(-1)^n (first column of unsigned triangle).

Cf. A047058, A051188, A051189, A051232, A035279.

Programs

Magma

[10^n*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Oct 05 2011

Maple

with(combstruct):A:=[N,{N=Cycle(Union(Z$10))},labeled]: seq(count(A,size=n)/10,n=0..14); # Zerinvary Lajos, Dec 05 2007

Mathematica

Array[#!*10^# &, 14, 0] (* Michael De Vlieger, Sep 04 2017 *)

Formula

a(n) = 10*A035279(n) = Product_{k=1..n} 10*k, n >= 1; a(0) := 1.

a(n) = n!*10^n =: (10*n)(!^10);

E.g.f.: 1/(1-10*x).

G.f.: 1/(1 - 10*x/(1 - 10*x/(1 - 20*x/(1 - 20*x/(1 - 30*x/(1 - 30*x/(1 - ...))))))), a continued fraction. - Ilya Gutkovskiy, May 12 2017

From Amiram Eldar, Jun 25 2020: (Start)

Sum_{n>=0} 1/a(n) = e^(1/10).

Sum_{n>=0} (-1)^n/a(n) = e^(-1/10). (End)