A392915 Expansion of e.g.f. -LambertW(-x*log(1-x)^2).

0, 0, 0, 6, 24, 110, 1320, 13916, 142464, 2049624, 33142320, 544496832, 10291564800, 218303448480, 4876345463808, 117792553680720, 3097357482401280, 86434348852857600, 2558467818878374656, 80688669655929224832, 2688349420757785743360, 94211227356606815454720, 3474423524089075296549888

Offset

0,4

Links

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

Formula

a(n) ~ sqrt(1 + 2*exp(1/2)*r^(3/2)/(1-r)) * n^(n-1) / (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[-LambertW[-x*Log[1-x]^2], {x, 0, nmax}], x] * Range[0, nmax]!

Crossrefs

Cf. A357265, A392824, A392916, A392918.

Sequence in context: A038380 A052745 A392823 * A392916 A392830 A392829

Adjacent sequences: A392912 A392913 A392914 * A392916 A392917 A392918

Keyword

nonn

Author

Vaclav Kotesovec, Jan 27 2026

Status

approved