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A335111
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a(n) = n! * Sum_{k=0..n-1} (-2)^k / k!.
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2
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0, 1, -2, 6, -8, 40, 48, 784, 5248, 49536, 490240, 5403904, 64822272, 842742784, 11798284288, 176974510080, 2831591636992, 48137058942976, 866467058614272, 16462874118651904, 329257482362552320, 6914407129635618816, 152116956851937476608, 3498690007594658430976
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OFFSET
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0,3
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COMMENTS
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Inverse binomial transform of A000240.
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} k! * x^k / (1 + 2*x)^(k + 1).
E.g.f.: x*exp(-2*x) / (1 - x).
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MATHEMATICA
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Table[n! Sum[(-2)^k/k!, {k, 0, n - 1}], {n, 0, 23}]
nmax = 23; CoefficientList[Series[Sum[k! x^k/(1 + 2 x)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 23; CoefficientList[Series[x Exp[-2 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
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PROG
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(PARI) a(n) = n! * sum(k=0, n-1, (-2)^k / k!); \\ Michel Marcus, May 23 2020
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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