A277466 -id:A277466 - cp's OEIS frontend

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

Vaclav Kotesovec, Oct 16 2016

nonn

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

Cf. A000312, A086331, A277466.

S:= series(log(1+x)/(1+LambertW(-x)), x, 51):
seq(coeff(S,x,n)*n!, n=0..50); # Robert Israel, Oct 26 2016

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

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

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

A277482 E.g.f.: log(1-x)*LambertW(-x).

Original entry on oeis.org

0, 0, 2, 9, 56, 480, 5394, 75775, 1280376, 25270056, 569899770, 14444562803, 406204015524, 12545427045008, 422007399953398, 15354968442741135, 600807449737710832, 25153741340051795248, 1121917008608064151218, 53107023489332468636739, 2658946993059795072656540

Offset: 0

Vaclav Kotesovec, Oct 17 2016

nonn

G. C. Greubel, Table of n, a(n) for n = 0..385

Cf. A000169, A277466, A277473, A277481.

CoefficientList[Series[Log[1-x]*LambertW[-x], {x, 0, 20}], x] * Range[0, 20]!
Table[n!*Sum[k^(k-1)/(k!*(n-k)), {k, 1, n-1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 28 2016 *)

x='x+O('x^50); concat([0,0], Vec(serlaplace(log(1-x)*lambertw(-x)) )) \\ G. C. Greubel, Nov 09 2017

a(n) ~ -log(1-exp(-1)) * n^(n-1).

cp's OEIS Frontend

A277465 Expansion of e.g.f. log(1+x)/(1 + LambertW(-x)).

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