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a(0)=0, for n >= 1, a(n) = (2^(n-1)-1)*n!.
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%I #19 Jul 06 2024 21:26:40

%S 0,0,2,18,168,1800,22320,317520,5120640,92534400,1854316800,

%T 40834886400,980516275200,25499650176000,714077383219200,

%U 21423629170944000,685577056260096000,23309975600271360000

%N a(0)=0, for n >= 1, a(n) = (2^(n-1)-1)*n!.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=612">Encyclopedia of Combinatorial Structures 612</a>

%F E.g.f.: x^2/((1-x)*(1-2*x)).

%F D-finite Recurrence: {a(1)=0, a(0)=0, a(2)=2, (2*n^2+6*n+4)*a(n)+(-6-3*n)*a(n+1)+a(n+2)}

%F a(n) = n!*A000225(n-1). - _R. J. Mathar_, Jun 03 2022

%p spec := [S,{S=Prod(Z,Z,Sequence(Z),Sequence(Union(Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%t Join[{0},Table[(2^(n-1)-1)n!,{n,20}]] (* or *) With[{nn=20}, CoefficientList[ Series[x^2/((1-x)(1-2x)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 29 2021 *)

%K easy,nonn

%O 0,3

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000