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%I #23 May 31 2022 22:28:15
%S 0,1,8,78,960,14520,262080,5508720,132249600,3571102080,107136691200,
%T 3535550726400,127280305152000,4963938127948800,208485488552140800,
%U 9381848292520704000,450328738963783680000,22966766042840395776000
%N Expansion of e.g.f. x/((1-x)*(1-3*x)).
%H G. C. Greubel, <a href="/A052698/b052698.txt">Table of n, a(n) for n = 0..375</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=648">Encyclopedia of Combinatorial Structures 648</a>
%F E.g.f.: x/((1-x)*(1-3*x)).
%F D-finite Recurrence: a(0) = 0, a(1)=1, a(n) = 4*n*a(n-1) - 3*n*(n-1)*a(n-2).
%F a(n) = (3^n - 1)*n!/2.
%F a(n) = n!*A003462(n). - _R. J. Mathar_, Nov 27 2011
%p spec := [S,{S=Prod(Z,Sequence(Z),Sequence(Union(Z,Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[x/((1-x)(1-3x)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 05 2014 *)
%t Table[(3^n-1)*n!/2, {n,0,30}] (* _G. C. Greubel_, May 31 2022 *)
%o (SageMath) [(3^n-1)*factorial(n)/2 for n in (0..30)] # _G. C. Greubel_, May 31 2022
%Y Cf. A003462.
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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