A294319 a(n) = Product_{k=0..n} (3*k + 2)!.

2, 240, 9676800, 386266890240000, 33674087438261157888000000, 11977449554394932435557703221248000000000, 29139961073721833036780987632259240162985246720000000000000

Offset: 0

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

• nonn

Crossrefs

Cf. A268504, A294318.

Programs

Mathematica

Table[Product[(3*k + 2)!, {k, 0, n}] , {n, 0, 10}]
FoldList[Times,(3 Range[0,10]+2)!] (* Harvey P. Dale, Sep 26 2023 *)

Formula

a(n) ~ 3^(3*n^2/2 + 4*n + 101/36) * (2*Pi)^(n/2 + 1/3) * n^(3*n^2/2 + 4*n + 91/36) * Gamma(1/3)^(1/3) / (A^(1/3) * exp(9*n^2/4 + 4*n - 1/36)), where A is the Glaisher-Kinkelin constant A074962.

A268504(n) * A294318(n) * A294319(n) = A000178(3*n + 2).