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A051232 9-factorial numbers.

%I A051232 #43 Aug 12 2024 01:28:20
%S A051232 1,9,162,4374,157464,7085880,382637520,24106163760,1735643790720,
%T A051232 140587147048320,12652843234348800,1252631480200531200,
%U A051232 135284199861657369600,15828251383813912243200,1994359674360552942643200,269238556038674647256832000
%N A051232 9-factorial numbers.
%C A051232 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
%C A051232 a(n) = 9*A035023(n) = Product_{k=1..n} 9*k, n >= 1; a(0) := 1.
%C A051232 Pi^n/a(n) is the volume of a 2n-dimensional ball with radius 1/3. - _Peter Luschny_, Jul 24 2012
%H A051232 Vincenzo Librandi, <a href="/A051232/b051232.txt">Table of n, a(n) for n = 0..300</a>
%H A051232 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A051232 a(n) = n!*9^n =: (9*n)(!^9).
%F A051232 E.g.f.: 1/(1-9*x).
%F A051232 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
%F A051232 From _Amiram Eldar_, Jun 25 2020: (Start)
%F A051232 Sum_{n>=0} 1/a(n) = e^(1/9).
%F A051232 Sum_{n>=0} (-1)^n/a(n) = e^(-1/9). (End)
%p A051232 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
%t A051232 s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 8, 2*5!, 9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%o A051232 (Magma) [9^n*Factorial(n): n in [0..20]]; // _Vincenzo Librandi_, Oct 05 2011
%Y A051232 Cf. A047058, A051188, A051189. a(n) = A051231(n-1, 0), A053116 (first column of triangle).
%K A051232 easy,nonn
%O A051232 0,2
%A A051232 _Wolfdieter Lang_