A392917 - OEIS

A392917

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

1, 0, 0, 0, 24, 180, 1260, 9450, 158592, 2886408, 48818640, 795900600, 15100696512, 340506408528, 8365904059968, 210351550631040, 5525898948117504, 156647992663952640, 4801451402037634560, 155541325317358671360, 5257296284868644774400, 185957621020707402343680, 6922596407357367956736000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

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

FORMULA

a(n) ~ n^n / (sqrt(1 + 3*exp(1/3)*r^(4/3)/(1-r)) * 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[1/(1+LambertW[x*Log[1-x]^3]), {x, 0, nmax}], x] * Range[0, nmax]!

CROSSREFS

Cf. A392916, A392918.

Sequence in context: A052758 A392824 A392918 * A392854 A241434 A143040

Adjacent sequences: A392914 A392915 A392916 * A392918 A392919 A392920

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jan 27 2026

STATUS

approved