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A277505
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E.g.f.: -LambertW(-x)/(1-x).
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3
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0, 1, 4, 21, 148, 1365, 15966, 229411, 3932440, 78438681, 1784386810, 45565679511, 1289796524820, 40065439945141, 1354630932486118, 49512390012682395, 1945119744809765296, 81728227537432878513, 3657019655412488345202, 173610723750748520091679
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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) = Sum_{k=1..n} binomial(n,k) * k^(k-1) * (n-k)!.
a(n) ~ n^(n-1) / (1-exp(-1)).
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MATHEMATICA
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CoefficientList[Series[-LambertW[-x]/(1-x), {x, 0, 20}], x] * Range[0, 20]!
Flatten[{0, Table[Sum[Binomial[n, k]*k^(k-1)*(n-k)!, {k, 1, n}], {n, 1, 20}]}]
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PROG
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(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(-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
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AUTHOR
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STATUS
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approved
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