%I A032031
%S A032031 1,3,18,162,1944,29160,524880,11022480,264539520,7142567040,
%T A032031 214277011200,7071141369600,254561089305600,9927882482918400,
%U A032031 416971064282572800,18763697892715776000,900657498850357248000
%N A032031 Triple factorial numbers: (3n)!!!=3^n*n!.
%C A032031 For n >= 1 a(n) is the order of the wreath product of the symmetric group 
               S_n and the elementary Abelian group (C_3)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), 
               May 07 2001
%C A032031 Laguerre transform of double factorials 2^n*n!=A000165(n). [From Paul 
               Barry (pbarry(AT)wit.ie), Aug 08 2008]
%D A032031 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.
%H A032031 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=491">
               Encyclopedia of Combinatorial Structures 491</a>
%H A032031 Alexsandar Petojevic, <a href="http://www.cs.uwaterloo.ca/journals/JIS/
               index.html">The Function vM_m(s; a; z) and Some Well-Known Sequences</
               a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
%F A032031 E.g.f.: 1/(1-3*x).
%F A032031 a(n)=sum{k=0..n, binomial(n,k)(n!/k!)2^k*k!}. [From Paul Barry (pbarry(AT)wit.ie), 
               Aug 08 2008]
%p A032031 with(combstruct):ZL:=[T,{T=Union(Z,Prod(Epsilon,Z,T),Prod(T,Z,Epsilon),
               Prod(T,Z))},labeled]:seq(count(ZL,size=i)/i,i=1..17); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2007
%p A032031 restart: G(x):=(1-3*x)^(n-2): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],
               x) od:x:=0:seq(f[n],n=0..16);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 04 2009]
%t A032031 Table[3^n*Gamma[1 + n], {n, 0, 20}] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), 
               Oct 30 2008
%t A032031 s=3;lst={1, s};Do[s+=n*s+s;AppendTo[lst, s], {n, 4, 5!, 3}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
%Y A032031 Cf. A000142, A007559, A008544, A051141, A000165.
%Y A032031 Sequence in context: A052182 A115415 A065058 this_sequence A127646 A089466 
               A107403
%Y A032031 Adjacent sequences: A032028 A032029 A032030 this_sequence A032032 A032033 
               A032034
%K A032031 nonn,easy,nice
%O A032031 0,2
%A A032031 Christian G. Bower (bowerc(AT)usa.net)