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

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..386

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

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

Mathematica

CoefficientList[Series[Log[1+x]/(1+LambertW[-x]), {x, 0, 25}], x] * Range[0, 25]!

Prog

(PARI) x='x+O('x^50); concat([0], Vec(serlaplace(log(1+x)/(1 + lambertw(-x))))) \\ G. C. Greubel, Nov 07 2017

Crossrefs

Cf. A000312, A086331, A277466.

Sequence in context: A080962 A243879 A298253 * A357535 A232078 A016222

Adjacent sequences: A277462 A277463 A277464 * A277466 A277467 A277468

Keyword

nonn

Author

Vaclav Kotesovec, Oct 16 2016

Status

approved