A316748 Stirling transform of (3*n)!.

1, 6, 726, 365046, 481183926, 1312473466806, 6422019989033526, 51225575261701080246, 621880652519326246083126, 10911229213845806303174823606, 265743324574322126992546955062326, 8697919110119969555113124407898635446, 372566878251517048881238923757823056246326

Offset: 0

Author

Vaclav Kotesovec, Jul 12 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..149
• Eric Weisstein's World of Mathematics, Stirling Transform.

Crossrefs

Cf. A000670, A064618, A316747, A353774.

Programs

Mathematica

Table[Sum[StirlingS2[n, k]*(3*k)!, {k, 0, n}], {n, 0, 15}]

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

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