OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..572
FORMULA
a(n) ~ sqrt(2*Pi/(1 + LambertW(exp(1)*n/3))) * n^(n + 1/2) * exp(n/LambertW(exp(1)*n/3) - n) / LambertW(exp(1)*n/3)^(n + 1/2).
G.f.: Sum_{k>=0} 3^k * x^k / (1 - k*x). - Ilya Gutkovskiy, Feb 06 2022
MATHEMATICA
Join[{1}, Table[Sum[3^k*k^(n-k), {k, 0, n}], {n, 1, 25}]]
PROG
(PARI) a(n) = sum(k=0, n, 3^k*k^(n-k)); \\ Michel Marcus, Feb 06 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 06 2022
STATUS
approved