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 A052659 Expansion of e.g.f. (1-2x)(1-x)/(1-4x+2x^2). 0

%I #16 Jul 28 2022 21:46:22

%S 1,1,8,84,1152,19680,403200,9636480,263208960,8087869440,276137164800,

%T 10370703974400,424893579264000,18858806481715200,901431900123955200,

%U 46165215285116928000,2521886466187984896000

%N Expansion of e.g.f. (1-2x)(1-x)/(1-4x+2x^2).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=606">Encyclopedia of Combinatorial Structures 606</a>

%F E.g.f.: (-1+2*x)*(-1+x)/(1-4*x+2*x^2).

%F Recurrence: {a(1)=1, a(0)=1, a(2)=8, (2*n^2+6*n+4)*a(n)+(-4*n-8)*a(n+1)+a(n+2)=0}.

%F Sum(-1/4*(-1+2*_alpha)*_alpha^(-1-n), _alpha=RootOf(1-4*_Z+2*_Z^2))*n!.

%F a(n) = n!*A007070(n-1). - _R. J. Mathar_, Nov 27 2011

%p spec := [S,{S=Sequence(Prod(Z,Sequence(Z),Sequence(Union(Z,Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%Y Cf. A007070.

%K easy,nonn

%O 0,3

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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