A294320 a(n) = Product_{k=0..n} (4*k + 1)!.

1, 120, 43545600, 271159356948480000, 96447974277170077976494080000000, 4927617876373416030299815278723491640115200000000000, 76433315893700635598991132508610825923227961061372903345356800000000000000000

Offset: 0

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

• nonn

Crossrefs

Cf. A168467, A268505, A294318, A294321, A294322.

Programs

Mathematica

Table[Product[(4*k + 1)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ 2^(4*n^2 + 15*n/2 + 10/3) * n^(2*n^2 + 7*n/2 + 65/48) * Pi^(n/2 + 3/4) / (A^(1/4) * Gamma(1/4)^(1/2) * exp(3*n^2 + 7*n/2 - 1/48)), where A is the Glaisher-Kinkelin constant A074962.

A268505(n) * A294320(n) * A294321(n) * A294322(n) = A000178(4*n + 3).