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A052700
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Expansion of e.g.f. x*(1-x)/(1-3*x).
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1
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0, 1, 4, 36, 432, 6480, 116640, 2449440, 58786560, 1587237120, 47617113600, 1571364748800, 56569130956800, 2206196107315200, 92660236507238400, 4169710642825728000, 200146110855634944000, 10207451653637382144000
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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)/(1-3*x)
D-finite recurrence: a(1)=1, a(0)=0, a(2)=4, a(n) = 3*n*a(n-1).
a(n) = 2*3^(n-2)*n! = 2*A153647(n-2), n>1.
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MAPLE
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spec := [S, {S=Prod(Z, Sequence(Prod(Sequence(Z), Union(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Table[2*3^(n-2)*n! -2*Boole[n==0]/9 + Boole[n==1]/3, {n, 0, 30}] (* G. C. Greubel, May 31 2022 *)
With[{nn=30}, CoefficientList[Series[x (1-x)/(1-3x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 19 2022 *)
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PROG
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(SageMath) [0, 1]+[2*3^(n-2)*factorial(n) for n in (2..30)] # G. C. Greubel, May 31 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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