OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k) * (3*k)!/(2*k+1)! * Stirling2(n,k).
a(n) ~ sqrt(69) * n^(n-1) / (2^(5/2) * log(27/23)^(n - 1/2) * exp(n)). - Vaclav Kotesovec, Nov 10 2023
MATHEMATICA
Table[Sum[(-1)^(n-k) * (3*k)!/(2*k+1)! * StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 10 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*(3*k)!/(2*k+1)!*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 07 2023
STATUS
approved