A268504 a(n) = Product_{k=0..n} (3*k)!.

1, 6, 4320, 1567641600, 750902834626560000, 981936389699695364014080000000, 6286723722110812136775527266768650240000000000, 321194638135877430211257700556824829511701622266265600000000000000

Offset

0,2

Comments

Partial products of A100732. - Michel Marcus, Jul 06 2019

Links

Seiichi Manyama, Table of n, a(n) for n = 0..22

Formula

a(n) ~ Gamma(1/3)^(1/3) * 3^(3*n^2/2 + 2*n + 11/36) * 2^(n/2 + 1/3) * Pi^(n/2 + 1/3) * n^(3*n^2/2 + 2*n + 19/36) / (A^(1/3) * exp(9*n^2/4 + 2*n - 1/36)), where A = A074962 is the Glaisher-Kinkelin constant.

Mathematica

Table[Product[(3*k)!, {k, 0, n}], {n, 0, 10}]

Prog

(PARI) {a(n) = prod(k=1, n, (3*k)!)} \\ Seiichi Manyama, Jul 06 2019

Crossrefs

Cf. A000178, A098694, A100732, A268196, A268505, A268506, A271946, A271947.

Sequence in context: A161845 A317485 A209310 * A099723 A226499 A343096

Adjacent sequences: A268501 A268502 A268503 * A268505 A268506 A268507

Keyword

nonn

Author

Vaclav Kotesovec, Apr 16 2016

Status

approved