OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: -LambertW(3 * (1 - exp(x)))/3.
a(n) = Sum_{k=1..n} (3 * k)^(k-1) * Stirling2(n,k).
a(n) ~ sqrt(1 + 3*exp(1)) * n^(n-1) / (3 * exp(n) * log(1 + exp(-1)/3)^(n - 1/2)). - Vaclav Kotesovec, Nov 14 2022
E.g.f.: Series_Reversion( log(1 + x * exp(-3*x)) ). - Seiichi Manyama, Sep 09 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(3*(1-exp(x)))/3)))
(PARI) a(n) = sum(k=1, n, (3*k)^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 24 2022
STATUS
approved