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A052579 E.g.f. (2+x+x^2)/((1-x)(1+x+x^2)).

%I A052579 #18 May 10 2019 18:09:49
%S A052579 2,1,2,12,24,120,1440,5040,40320,725760,3628800,39916800,958003200,
%T A052579 6227020800,87178291200,2615348736000,20922789888000,355687428096000,
%U A052579 12804747411456000,121645100408832000,2432902008176640000
%N A052579 E.g.f. (2+x+x^2)/((1-x)(1+x+x^2)).
%H A052579 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=523">Encyclopedia of Combinatorial Structures 523</a>
%F A052579 E.g.f.: -(x^2+x+2)/(-1+x)/(1+x+x^2)
%F A052579 Recurrence: {a(1)=1, a(2)=2, a(0)=2, (-11*n-6-n^3-6*n^2)*a(n)+a(n+3)=0}
%F A052579 (4/3+Sum(1/3*_alpha^(-n), _alpha=RootOf(_Z^2+_Z+1)))*n!
%F A052579 a(n) = n!*A131534(n+1). - _R. J. Mathar_, Nov 27 2011
%p A052579 spec := [S,{S=Union(Sequence(Prod(Z,Z,Z)), Sequence(Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052579 With[{nn=20},CoefficientList[Series[(2+x+x^2)/((1-x)(1+x+x^2)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 10 2019 *)
%K A052579 easy,nonn
%O A052579 0,1
%A A052579 encyclopedia(AT)pommard.inria.fr, Jan 25 2000