A316748 Stirling transform of (3*n)!.

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

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

Cf. A000670, A064618, A316747, A353774.

Sequence in context: A343434 A202080 A271528 * A354251 A232130 A289365

Adjacent sequences: A316745 A316746 A316747 * A316749 A316750 A316751

Keyword

nonn

Author

Vaclav Kotesovec, Jul 12 2018

Status

approved