A294318 a(n) = Product_{k=0..n} (3*k + 1)!.

1, 24, 120960, 438939648000, 2733286318040678400000, 57187975336110258000180019200000000, 6956637001938940278070327452315517609574400000000000, 7819265053064003641840525064819521833578308036969094971392000000000000000

Offset: 0

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

• nonn

Crossrefs

Cf. A168467, A268504, A294319.

Programs

Mathematica

Table[Product[(3*k + 1)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ 3^(3*n^2/2 + 3*n + 47/36) * n^(3*n^2/2 + 3*n + 49/36) * (2*Pi)^(n/2 + 5/6) / (A^(1/3) * Gamma(1/3)^(2/3) * exp(9*n^2/4 + 3*n - 1/36)), where A is the Glaisher-Kinkelin constant A074962.

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