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A052653 E.g.f. (1-2x^2)/(1-x-2x^2). 0

%I #15 Apr 18 2017 07:03:58

%S 1,1,2,18,120,1320,15120,216720,3427200,62052480,1237420800,

%T 27263174400,653837184000,17005993804800,476080648243200,

%U 14283727121664000,457058345103360000,15540339420942336000

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

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=600">Encyclopedia of Combinatorial Structures 600</a>

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

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

%F Sum(-1/9*(-2+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+2*_Z^2))*n!

%F a(n) = n!*A001045(n), n>0. - _R. J. Mathar_, Nov 27 2011

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

%t With[{nn=20},CoefficientList[Series[(1-2x^2)/(1-x-2x^2),{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Feb 13 2013 *)

%K easy,nonn

%O 0,3

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

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Last modified April 23 22:36 EDT 2024. Contains 371917 sequences. (Running on oeis4.)