cp's OEIS Frontend

A052613 E.g.f. (1-2x)/(1-2x-x^2+x^3).

%I A052613 #15 Jun 03 2022 18:48:06
%S A052613 1,0,2,6,72,720,10080,156240,2822400,56972160,1280966400,31654022400,
%T A052613 853580851200,24932991283200,784343085926400,26435945023488000,
%U A052613 950417730662400000,36304660098330624000,1468365202287599616000
%N A052613 E.g.f. (1-2x)/(1-2x-x^2+x^3).
%H A052613 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=558">Encyclopedia of Combinatorial Structures 558</a>
%F A052613 E.g.f.: -(-1+2*x)/(x^3-x^2-2*x+1)
%F A052613 Recurrence: {a(1)=0, a(0)=1, a(2)=2, (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}
%F A052613 Sum(1/7*(-1+3*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))*n!
%F A052613 a(n)=n!*A077998(n-2), n>=2. - _R. J. Mathar_, Jun 03 2022
%p A052613 spec := [S,{S=Sequence(Prod(Z,Z,Sequence(Prod(Z,Sequence(Z)))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052613 With[{nn=20},CoefficientList[Series[(1-2x)/(1-2x-x^2+x^3),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 08 2015 *)
%K A052613 easy,nonn
%O A052613 0,3
%A A052613 encyclopedia(AT)pommard.inria.fr, Jan 25 2000