OFFSET
0,4
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(n-3*k)/(n-3*k)!.
a(n) == 1 (mod 6).
a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / ((1 + LambertW(1/3)) * 3^(n+4) * exp(n) * LambertW(1/3)^(n+3)). - Vaclav Kotesovec, Aug 21 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x)-x^3)))
(PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(n-3*k)/(n-3*k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 21 2024
STATUS
approved