OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..149
Eric Weisstein's World of Mathematics, Stirling Transform.
FORMULA
a(n) ~ (3*n)!.
a(n) ~ sqrt(2*Pi) * 3^(3*n + 1/2) * n^(3*n + 1/2) / exp(3*n).
E.g.f.: Sum_{k>=0} (3*k)! * (exp(x) - 1)^k / k!. - Seiichi Manyama, May 21 2022
MATHEMATICA
Table[Sum[StirlingS2[n, k]*(3*k)!, {k, 0, n}], {n, 0, 15}]
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k)!*(exp(x)-1)^k/k!))) \\ Seiichi Manyama, May 21 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 12 2018
STATUS
approved