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%I #15 Dec 01 2018 11:16:01
%S 1,2,8,42,288,2400,23760,272160,3548160,51891840,841881600,
%T 15008716800,291711974400,6139842508800,139136552755200,
%U 3377722892544000,87457261731840000,2405869763641344000
%N E.g.f. 1/((1-x)(1-x-x^2)).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=592">Encyclopedia of Combinatorial Structures 592</a>
%F E.g.f.: 1/(-1+x)/(-1+x+x^2)
%F Recurrence: {a(0)=1, a(1)=2, a(2)=8, (n^3+6*n^2+11*n+6)*a(n)+(-2*n-6)*a(n+2)+a(n+3)=0}
%F (-1+Sum(1/5*(4+3*_alpha)*_alpha^(-1-n), _alpha =RootOf(-1+_Z+_Z^2)))*n!
%F n!*Sum(k=0, n, A000045(n+1)).
%F a(n) = n!*A000071(n+3). - _R. J. Mathar_, Nov 27 2011
%p spec := [S,{S=Prod(Sequence(Z),Sequence(Union(Z,Prod(Z,Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[1/((1-x)(1-x-x^2)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 01 2018 *)
%K easy,nonn
%O 0,2
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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