OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} 3^k * (k+1)! * |Stirling1(n,k)|.
a(0) = 1; a(n) = 3 * Sum_{k=1..n} (k/n + 1) * (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ sqrt(2*Pi) * n^(n + 3/2) / (9 * exp(2*n/3) * (exp(1/3) - 1)^(n+2)). - Vaclav Kotesovec, Sep 06 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*log(1-x))^2))
(PARI) a(n) = sum(k=0, n, 3^k*(k+1)!*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2024
STATUS
approved