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A052581 E.g.f. (1-x)/(1-x-x^4).

%I A052581 #20 Aug 24 2017 20:56:04
%S A052581 1,0,0,0,24,120,720,5040,80640,1088640,14515200,199584000,3353011200,
%T A052581 62270208000,1220496076800,24845812992000,543992537088000,
%U A052581 12804747411456000,320118685286400000,8393511928209408000
%N A052581 E.g.f. (1-x)/(1-x-x^4).
%C A052581 Except for an initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - S)(1 - 2 S); see A291000.  - _Clark Kimberling_, Aug 24 2017
%H A052581 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=525">Encyclopedia of Combinatorial Structures 525</a>
%F A052581 E.g.f.: (-1+x)/(-1+x^4+x)
%F A052581 Recurrence: {a(1)=0, a(0)=1, a(2)=0, a(3)=0, (-n^4-35*n^2-50*n-24-10*n^3)*a(n) +(-n-4)*a(n+3) +a(n+4)=0}
%F A052581 Sum(-1/283*(9+12*_alpha^3+16*_alpha^2-73*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^4+_Z))*n!
%F A052581 a(n)= n!*A017898(n). - _R. J. Mathar_, Nov 27 2011
%p A052581 spec := [S,{S=Sequence(Prod(Z,Z,Z,Z,Sequence(Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052581 With[{nn=20},CoefficientList[Series[(1-x)/(1-x-x^4),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 27 2016 *)
%K A052581 easy,nonn
%O A052581 0,5
%A A052581 encyclopedia(AT)pommard.inria.fr, Jan 25 2000