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%I #19 Jun 03 2022 18:33:58
%S 1,2,8,60,576,6960,100800,1703520,32901120,714873600,17258572800,
%T 458324697600,13277924352000,416724685977600,14084873439436800,
%U 510058387238400000,19702238017093632000,808611973910028288000
%N E.g.f. (1-x^2)/(1-2x-x^2).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=568">Encyclopedia of Combinatorial Structures 568</a>
%F E.g.f.: (-1+x^2)/(-1+2*x+x^2)
%F Recurrence: {a(0)=1, a(1)=2, a(2)=8, (-2-n^2-3*n)*a(n) +(-4-2*n)*a(n+1) +a(n+2)=0}
%F Sum(-1/2*(-1+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^2))*n!
%F a(n) = n!*((1+sqrt(2))^n - (1-sqrt(2))^n)/sqrt(2). - _Vaclav Kotesovec_, Oct 05 2013
%F a(n)=n!*A052542(n). - _R. J. Mathar_, Jun 03 2022
%p spec := [S,{S=Sequence(Prod(Union(Z,Z),Sequence(Prod(Z,Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[(1-x^2)/(1-2x-x^2),{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Mar 04 2013 *)
%K easy,nonn
%O 0,2
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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