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%I #26 Dec 10 2024 08:59:00
%S 1,1,4,30,264,3000,40320,635040,11410560,230791680,5185555200,
%T 128172844800,3455996544000,100952461209600,3175730791833600,
%U 107037070043904000,3848161361780736000,146994587721805824000
%N Expansion of e.g.f. (1-x^2)*(1-x)/(1-2x-x^2+x^3).
%H Vincenzo Librandi, <a href="/A052658/b052658.txt">Table of n, a(n) for n = 0..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=605">Encyclopedia of Combinatorial Structures 605</a>
%F E.g.f.: (-1+x^2)*(-1+x)/(x^3-x^2-2*x+1)
%F Recurrence: {a(1)=1, a(0)=1, a(2)=4, (n^3+6*n^2+11*n+6)*a(n)+(-n^2-5*n-6)*a(n+1)+(-2*n-6)*a(n+2)+a(n+3)=0, a(3)=30}
%F a(n) = Sum(-1/7*(_alpha+_alpha^2-2)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))*n!.
%F a(n) = n!*A006054(n+1),n>0. - _R. J. Mathar_, Jun 03 2022
%p spec := [S,{S=Sequence(Prod(Z,Sequence(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-x))/(1-2x-x^2+x^3),{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, May 16 2012 *)
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000