OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} 3^(n-k) * (Product_{j=0..k-1} (3*j+1)) * |Stirling1(n,k)|.
a(0) = 1; a(n) = Sum_{k=1..n} 3^k * (1 - 2/3 * k/n) * (k-1)! * binomial(n,k) * a(n-k).
PROG
(PARI) a(n) = sum(k=0, n, 3^(n-k)*prod(j=0, k-1, 3*j+1)*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 18 2023
STATUS
approved