A051232 9-factorial numbers.

1, 9, 162, 4374, 157464, 7085880, 382637520, 24106163760, 1735643790720, 140587147048320, 12652843234348800, 1252631480200531200, 135284199861657369600, 15828251383813912243200, 1994359674360552942643200, 269238556038674647256832000

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_9)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001

a(n) = 9*A035023(n) = Product_{k=1..n} 9*k, n >= 1; a(0) := 1.

Pi^n/a(n) is the volume of a 2n-dimensional ball with radius 1/3. - Peter Luschny, Jul 24 2012

Links

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

Crossrefs

Cf. A047058, A051188, A051189. a(n) = A051231(n-1, 0), A053116 (first column of triangle).

Programs

Magma

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

Maple

with(combstruct):A:=[N,{N=Cycle(Union(Z$9))},labeled]: seq(count(A,size=n+1)/9, n=0..14); # Zerinvary Lajos, Dec 05 2007

Mathematica

s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 8, 2*5!, 9}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)

Formula

a(n) = n!*9^n =: (9*n)(!^9).

E.g.f.: 1/(1-9*x).

G.f.: 1/(1 - 9*x/(1 - 9*x/(1 - 18*x/(1 - 18*x/(1 - 27*x/(1 - 27*x/(1 - ...))))))), a continued fraction. - Ilya Gutkovskiy, Aug 09 2017

From Amiram Eldar, Jun 25 2020: (Start)

Sum_{n>=0} 1/a(n) = e^(1/9).

Sum_{n>=0} (-1)^n/a(n) = e^(-1/9). (End)