A294325 a(n) = Product_{k=0..n} (5*k + 3)!.

6, 241920, 1506440871936000, 9644797427717007797649408000000, 249337464544494851133170653103408676989829120000000000, 76020086814652932482688746849816272353956621412690696880710462996480000000000000000

Offset: 0

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

• nonn

Crossrefs

Cf. A268506, A294322, A294323, A294324, A294326.

Programs

Mathematica

Table[Product[(5*k + 3)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ (1 + sqrt(5))^(2/5) * Gamma(2/5)^(1/5) * 2^(n/2 + 1/5) * 5^(5*n^2/2 + 6*n + 43/12) * n^(5*n^2/2 + 6*n + 203/60) * Pi^(n/2 + 3/5) / (A^(1/5) * Gamma(1/5)^(2/5) * exp(15*n^2/4 + 6*n - 1/60)), where A is the Glaisher-Kinkelin constant A074962.

A268506(n) * A294323(n) * A294324(n) * A294325(n) * A294326(n) = A000178(5*n+4).