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A052575
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Expansion of e.g.f. (1-x)/(1-2*x-2*x^2+2*x^3).
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1
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1, 1, 8, 48, 528, 6240, 95040, 1632960, 32578560, 725760000, 18027878400, 491774976000, 14645952921600, 472356889804800, 16409046682828800, 610694391250944000, 24244324628299776000, 1022626965270822912000
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: (1-x)/(1-2*x-2*x^2+2*x^3).
(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.
Sum_(-1/37*(-5+9*_alpha^2-12*_alpha)*_alpha^(-1-n), _alpha=RootOf(2*_Z^3-2*_Z^2-2*_Z+1))*n!.
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MAPLE
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spec := [S, {S=Sequence(Prod(Z, Union(Z, Z, Sequence(Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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