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%I #16 Jun 03 2022 18:53:59
%S 0,1,0,0,24,120,720,10080,120960,1451520,21772800,359251200,
%T 6227020800,118313395200,2440992153600,53614649088000,
%U 1255367393280000,31300493672448000,825906208038912000
%N Expansion of E.g.f. x*(1-x)/(1-x-x^3).
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=550">Encyclopedia of Combinatorial Structures 550</a>
%F E.g.f.: x*(-1+x)/(-1+x+x^3).
%F Recurrence: a(1)=1, a(0)=0, a(2)=0, (-11*n-6-n^3-6*n^2)*a(n) +(-n-3)*a(n+2) +a(n+3) = 0.
%F Sum(1/31*(_alpha+11*_alpha^2-3)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^3))*n!.
%F a(n)=n!*A078012(n-1). - _R. J. Mathar_, Jun 03 2022
%p spec := [S,{S=Prod(Z,Sequence(Prod(Z,Z,Z,Sequence(Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%K easy,nonn
%O 0,5
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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