A277465 Expansion of e.g.f. log(1+x)/(1 + LambertW(-x)).
0, 1, 1, 11, 86, 1084, 15654, 275113, 5548024, 127423728, 3272008650, 92988690893, 2896148079516, 98104636748468, 3590611928294286, 141201205469361945, 5937400341113630032, 265833516437952849024, 12625912572901413474834, 634047172218326393377149
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..386
Programs
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Maple
S:= series(log(1+x)/(1+LambertW(-x)), x, 51): seq(coeff(S,x,n)*n!, n=0..50); # Robert Israel, Oct 26 2016
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Mathematica
CoefficientList[Series[Log[1+x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]! -
PARI
x='x+O('x^50); concat([0],Vec(serlaplace(log(1+x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 07 2017
Formula
E.g.f.: log(1+x)/(1 + LambertW(-x)).
a(n) ~ log(1+exp(-1)) * n^n.
a(n) = (-1)^(n+1)*(n-1)! + Sum_{j=1..n-1} a(j)*binomial(n,j)*(n-j)^(n-j-1). - Robert Israel, Oct 26 2016