OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = Sum_{k=1..n} 3^(n-k) * k^(k-1) * Stirling2(n,k).
a(n) ~ 3^(n - 1/2) * sqrt(exp(1) + 3) * n^(n-1) / (exp(n) * (log(exp(1) + 3) - 1)^(n - 1/2)). - Vaclav Kotesovec, Oct 04 2022
E.g.f.: Series_Reversion( (log(1 + 3 * x * exp(-x)))/3 ). - Seiichi Manyama, Sep 11 2024
MATHEMATICA
With[{m = 20}, Range[0, m]! * CoefficientList[Series[-ProductLog[(1 - Exp[3*x])/3], {x, 0, m}], x]] (* Amiram Eldar, Sep 24 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw((1-exp(3*x))/3))))
(PARI) a(n) = sum(k=1, n, 3^(n-k)*k^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 24 2022
STATUS
approved