OFFSET
0,5
FORMULA
G.f.: Sum_{k>=0} x^k / (1 - k * x^3).
a(n) ~ sqrt(2*Pi/3) * (n/LambertW(exp(1)*n))^(n*(1 - 1/LambertW(exp(1)*n))/3 + 1/2) / sqrt(1 + LambertW(exp(1)*n)). - Vaclav Kotesovec, Apr 14 2022
PROG
(PARI) a(n) = sum(k=0, n\3, (n-3*k)^k);
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-k*x^3)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 09 2022
STATUS
approved