OFFSET
0,2
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
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)
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 *)
PROG
(Magma) [9^n*Factorial(n): n in [0..20]]; // Vincenzo Librandi, Oct 05 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved