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A277509
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Expansion of e.g.f. 1/((1+LambertW(-x))*(1+x)).
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5
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1, 0, 4, 15, 196, 2145, 33786, 587041, 12080888, 278692497, 7213075030, 205967845281, 6444486304884, 219096784628761, 8044651840755362, 317224112769528945, 13371158269397088496, 599930571306586259745, 28547657791777984900014, 1436014157616531876023713
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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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For n > 0, a(n) = (-1)^n*n!+Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * k^k * (n-k)!.
a(n) ~ n^n / (1+exp(-1)).
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MATHEMATICA
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CoefficientList[Series[1/(1+LambertW[-x])/(1+x), {x, 0, 20}], x] * Range[0, 20]!
Flatten[{1, Table[(-1)^n*n! + Sum[(-1)^(n-k) * Binomial[n, k] * k^k * (n-k)!, {k, 1, n}], {n, 1, 20}]}]
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PROG
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(PARI) my(x='x+O('x^50)); Vec(serlaplace(1/((1 + lambertw(-x))*(1+x)))) \\ G. C. Greubel, Nov 12 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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