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A009306
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Expansion of e.g.f.: log(1 + exp(x)*x).
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19
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0, 1, 1, -1, -2, 9, 6, -155, 232, 3969, -20870, -118779, 1655028, 1610257, -143697722, 522358005, 13332842416, -138189937791, -1128293525646, 29219838555781, 17274118159180, -5993074252801839, 38541972209299966, 1179892974640047669
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = n - Sum_{k=1..n-1} binomial(n-1,k-1) * (n-k) * a(k). - Ilya Gutkovskiy, Jan 17 2020
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MAPLE
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a:= n-> n! *add(k^(n-k-1) *(-1)^(k+1) /(n-k)!, k=1..n):
seq(a(n), n=0..25);
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Log[1+Exp[x]x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 22 2016 *)
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PROG
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(PARI) seq(n)=Vec(serlaplace(log(1 + exp(x + O(x^n))*x)), -(n+1)) \\ Andrew Howroyd, May 26 2021
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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