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A052580 E.g.f. (1-2x)/(1-2x-x^2). 0

%I

%S 1,0,2,12,120,1440,20880,352800,6814080,148055040,3574368000,

%T 94922150400,2749948185600,86306508288000,2917072801843200,

%U 105636550795776000,4080467097907200000,167469023145295872000

%N E.g.f. (1-2x)/(1-2x-x^2).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=524">Encyclopedia of Combinatorial Structures 524</a>

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

%F Recurrence: {a(1)=0, a(0)=1, (-2-n^2-3*n)*a(n)+(-4-2*n)*a(n+1)+a(n+2)=0.}

%F Sum(1/4*(-1+3*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+2*_Z+_Z^2))*n!

%F a(n) = n!*A000129(n-1). - _R. J. Mathar_, Nov 27 2011

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

%t With[{nn=20},CoefficientList[Series[(1-2x)/(1-2x-x^2),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Dec 05 2018 *)

%K easy,nonn

%O 0,3

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

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Last modified July 27 05:26 EDT 2021. Contains 346305 sequences. (Running on oeis4.)