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A052621 E.g.f. (2+x+x^2+x^3)/(1-x^4).

%I A052621 #16 Oct 10 2023 10:55:52
%S A052621 2,1,2,6,48,120,720,5040,80640,362880,3628800,39916800,958003200,
%T A052621 6227020800,87178291200,1307674368000,41845579776000,355687428096000,
%U A052621 6402373705728000,121645100408832000,4865804016353280000
%N A052621 E.g.f. (2+x+x^2+x^3)/(1-x^4).
%H A052621 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=567">Encyclopedia of Combinatorial Structures 567</a>
%F A052621 E.g.f.: -(x^3+x^2+x+2)/(-1+x^4)
%F A052621 Recurrence: {a(1)=1, a(3)=6, a(2)=2, a(0)=2, (-n^4-35*n^2-50*n-24-10*n^3)*a(n)+a(n+4)=0}
%F A052621 Sum(1/4*(_alpha^3+_alpha^2+2*_alpha+1)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^4))*n!
%F A052621 2n! if n is 0 mod 4, n! otherwise.
%F A052621 a(n)=n!*A177704(n+3). - _R. J. Mathar_, Jun 03 2022
%p A052621 spec := [S,{S=Union(Sequence(Z), Sequence(Prod(Z,Z,Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052621 With[{nn=20},CoefficientList[Series[(2+x+x^2+x^3)/(1-x^4),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 10 2023 *)
%K A052621 easy,nonn
%O A052621 0,1
%A A052621 encyclopedia(AT)pommard.inria.fr, Jan 25 2000