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A052690
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Expansion of e.g.f. x*(1+x-3*x^2)/(1-3*x).
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1
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0, 1, 8, 54, 648, 9720, 174960, 3674160, 88179840, 2380855680, 71425670400, 2357047123200, 84853696435200, 3309294160972800, 138990354760857600, 6254565964238592000, 300219166283452416000, 15311177480456073216000
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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.: x*(1 + x - 3*x^2)/(1 - 3*x).
Recurrence: a(0)=0, a(1)=1, a(2)=8, a(n) = 3*n*a(n-1).
a(n) = 3^(n-1)*n!, n>2.
G.f.: -1/3 + 2*x^2 + Hypergeometric2F0([1,1], [], 3*x). - G. C. Greubel, Jun 02 2022
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MAPLE
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spec := [S, {S=Prod(Z, Union(Z, Sequence(Union(Z, Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[x (1+x-3x^2)/(1-3x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 05 2018 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); [0] cat Coefficients(R!(Laplace( x*(1+x-3*x^2)/(1-3*x) ))); // G. C. Greubel, Jun 02 2022
(SageMath) [3^(n-1)*factorial(n) -bool(n==0)/3 +2*bool(n==2) for n in (0..30)] # G. C. Greubel, Jun 02 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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