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A052575 Expansion of e.g.f. (1-x)/(1-2*x-2*x^2+2*x^3).

%I A052575 #29 Mar 07 2022 07:56:01
%S A052575 1,1,8,48,528,6240,95040,1632960,32578560,725760000,18027878400,
%T A052575 491774976000,14645952921600,472356889804800,16409046682828800,
%U A052575 610694391250944000,24244324628299776000,1022626965270822912000
%N A052575 Expansion of e.g.f. (1-x)/(1-2*x-2*x^2+2*x^3).
%H A052575 Robert Israel, <a href="/A052575/b052575.txt">Table of n, a(n) for n = 0..390</a>
%H A052575 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=518">Encyclopedia of Combinatorial Structures 518</a>.
%F A052575 E.g.f.: (1-x)/(1-2*x-2*x^2+2*x^3).
%F A052575 (12+2*n^3+12*n^2+22*n)*a(n) + (-2*n^2-10*n-12)*a(n+1) + (-2*n-6)*a(n+2) + a(n+3) = 0, with a(1)=1, a(0)=1, a(2)=8.
%F A052575 Sum_(-1/37*(-5+9*_alpha^2-12*_alpha)*_alpha^(-1-n), _alpha=RootOf(2*_Z^3-2*_Z^2-2*_Z+1))*n!.
%F A052575 a(n) = n!*A052528(n). - _R. J. Mathar_, Nov 27 2011
%p A052575 spec := [S,{S=Sequence(Prod(Z,Union(Z,Z,Sequence(Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052575 m = 17; Range[0, m]! * CoefficientList[Series[(1 - x)/(1 - 2*x - 2*x^2 + 2*x^3), {x, 0, m}], x] (* _Amiram Eldar_, Mar 07 2022 *)
%o A052575 (PARI) my(x='x+O('x^25)); Vec(serlaplace((1-x)/(1-2*x-2*x^2+2*x^3))) \\ _Michel Marcus_, Mar 07 2022
%Y A052575 Cf. A052528.
%K A052575 easy,nonn
%O A052575 0,3
%A A052575 encyclopedia(AT)pommard.inria.fr, Jan 25 2000