A294323 a(n) = Product_{k=0..n} (5*k + 1)!.

1, 720, 28740096000, 601322989968949248000000, 30722158107023001697205508762501120000000000, 12389984031943899068723274670059592852478855603111854080000000000000000

Offset: 0

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

• nonn

Crossrefs

Cf. A168467, A268506, A294318, A294320, A294324, A294325, A294326.

Programs

Mathematica

Table[Product[(5*k + 1)!, {k, 0, n}] , {n, 0, 10}]

Formula

a(n) ~ 2^(n/2 + 7/10) * 5^(5*n^2/2 + 4*n + 4/3) * n^(5*n^2/2 + 4*n + 83/60) * Pi^(n/2 + 3/5) * Gamma(2/5)^(1/5) / (A^(1/5) * (1 + sqrt(5))^(1/10) * Gamma(1/5)^(2/5) * exp(15*n^2/4 + 4*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).