OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} 3^(n-k) * (Product_{j=0..k-1} (3*j+2)) * |Stirling1(n,k)|.
a(0) = 1; a(n) = Sum_{k=1..n} 3^k * (1 - 1/3 * k/n) * (k-1)! * binomial(n,k) * a(n-k).
MATHEMATICA
With[{nn=20}, CoefficientList[Series[1/(1+Log[1-3x])^(2/3), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 16 2024 *)
PROG
(PARI) a(n) = sum(k=0, n, 3^(n-k)*prod(j=0, k-1, 3*j+2)*abs(stirling(n, k, 1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 18 2023
STATUS
approved