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%I #13 Jun 03 2022 18:52:48
%S 1,1,8,78,984,15480,292320,6441120,162207360,4595512320,144662112000,
%T 5009199148800,189221439052800,7743449813299200,341258374762905600,
%U 16113703632009984000,811588993992032256000,43431603596770701312000
%N E.g.f. (1-x)^3/(1-4x+3x^2-x^3).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=548">Encyclopedia of Combinatorial Structures 548</a>
%F E.g.f.: (-1+x)^3/(-1+4*x-3*x^2+x^3)
%F Recurrence: {a(1)=1, a(0)=1, a(2)=8, (-11*n-6-n^3-6*n^2)*a(n)+(18+3*n^2+15*n)*a(n+1)+(-4*n-12)*a(n+2)+a(n+3)=0, a(3)=78}
%F Sum(-1/31*(5*_alpha+3*_alpha^2-6)*_alpha^(-1-n), _alpha=RootOf(-1+4*_Z-3*_Z^2+_Z^3))*n!
%F a(n)=n!*A052529(n). - _R. J. Mathar_, Jun 03 2022
%p spec := [S,{S=Sequence(Prod(Z,Sequence(Z),Sequence(Z),Sequence(Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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