A392918 - OEIS

A392918

Expansion of e.g.f. -LambertW(x*log(1-x)^3).

0, 0, 0, 0, 24, 180, 1260, 9450, 118272, 1797768, 27953040, 436649400, 7650225792, 155122810128, 3479472910368, 82098922127040, 2040626757717504, 54437258118032640, 1565384085435951360, 47856936296691740160, 1537781100405048691200, 51873695680970675393280, 1841906898046198734220800

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OFFSET

0,5

COMMENTS

It differs from A392824 starting at a(12).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..410

FORMULA

a(n) ~ sqrt(1 + 3*exp(1/3)*r^(4/3)/(1-r)) * n^(n-1) / (exp(n) * r^n), where r = 0.5771048115344214677569600335478490644999230519... is the root of the equation r*log(1-r)^3 = -exp(-1).

MATHEMATICA

nmax = 25; CoefficientList[Series[-LambertW[x*Log[1-x]^3], {x, 0, nmax}], x] * Range[0, nmax]!

CROSSREFS

Cf. A392824, A392915, A392917.

Sequence in context: A214310 A052758 A392824 * A392917 A392854 A241434

Adjacent sequences: A392915 A392916 A392917 * A392919 A392920 A392921

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jan 27 2026

STATUS

approved