OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (3*j+2)) * Stirling1(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (3 - k/n) * (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ Gamma(1/3) * n^(n + 1/6) / (3^(1/6) * sqrt(2*Pi) * (exp(1/3) - 1)^(n + 2/3) * exp(n - 2/9)). - Vaclav Kotesovec, Nov 11 2023
MATHEMATICA
a[n_] := Sum[Product[3*j + 2, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Sep 13 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, prod(j=0, k-1, 3*j+2)*stirling(n, k, 1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 11 2023
STATUS
approved