OFFSET
0,3
FORMULA
a(n) = Sum_{k=1..n} (3 * n)^(k-1) * Stirling2(n,k).
a(n) ~ n^(n-1) / (3 * sqrt(1 + LambertW(1/3)) * LambertW(1/3)^n * exp(n*(4 - 1/LambertW(1/3)))). - Vaclav Kotesovec, Nov 14 2022
E.g.f.: Series_Reversion( exp(-3*x) * log(1 + x) ). - Seiichi Manyama, Sep 10 2024
MATHEMATICA
Table[Sum[(3*n)^(k-1) * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 14 2022 *)
PROG
(PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 26 2022
STATUS
approved