A392916 Expansion of e.g.f. 1/(1 + LambertW(-x*log(1-x)^2)).

1, 0, 0, 6, 24, 110, 2040, 23996, 256704, 4408344, 80422560, 1410691392, 29349239040, 683578452960, 16333290931776, 422615215344240, 11925279751472640, 353550440382854400, 11074363473491430912, 369496344948612488064, 12971801850898908856320, 477346981891862854679040

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

a(n) ~ n^n / (sqrt(1 + 2*exp(1/2)*r^(3/2)/(1-r)) * exp(n) * r^n), where r = 0.55649932684118223515411845920949612663857069... is the root of the equation r*log(1-r)^2 = exp(-1).

Mathematica

nmax = 25; CoefficientList[Series[1/(1+LambertW[-x*Log[1-x]^2]), {x, 0, nmax}], x] * Range[0, nmax]!

Crossrefs

Cf. A362835, A392915, A392917.

Sequence in context: A052745 A392823 A392915 * A392830 A392829 A392760

Adjacent sequences: A392913 A392914 A392915 * A392917 A392918 A392919

Keyword

nonn

Author

Vaclav Kotesovec, Jan 27 2026

Status

approved