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

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

Offset: 0

Author

Vaclav Kotesovec, Apr 16 2016

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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.