OFFSET
0,3
FORMULA
a(n) = (1/(3*n+1)!) * Sum_{k=0..n} (3*n+k)! * Stirling1(n,k).
a(n) ~ LambertW(3*exp(2))^n * n^(n-1) / (sqrt(3*(1 + LambertW(3*exp(2)))) * exp(n) * (3 - LambertW(3*exp(2)))^(4*n + 1)). - Vaclav Kotesovec, Nov 07 2023
MATHEMATICA
Table[1/(3*n+1)! * Sum[(3*n+k)! * StirlingS1[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 07 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (3*n+k)!*stirling(n, k, 1))/(3*n+1)!;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 06 2023
STATUS
approved