A294322 a(n) = Product_{k=0..n} (4*k + 3)!.

6, 30240, 1207084032000, 1578472848668491776000000, 192013488168893760607534429765632000000000, 4963935910233933921764132479991824059486720994836480000000000000

Offset: 0

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

• nonn

Crossrefs

Cf. A268505, A294320, A294321, A294325.

Programs

Mathematica

Table[Product[(4*k + 3)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ 2^(4*n^2 + 23*n/2 + 47/6) * n^(2*n^2 + 11*n/2 + 173/48) * Pi^(n/2 + 1/4) * Gamma(1/4)^(1/2) / (A^(1/4) * exp(3*n^2 + 11*n/2 - 1/48)), where A is the Glaisher-Kinkelin constant A074962.

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