A294324 a(n) = Product_{k=0..n} (5*k + 2)!.

2, 10080, 4828336128000, 1717378459351319052288000000, 1930334638180469242638816526565470371840000000000, 21019161870767674789722561439867977128887689291877548419973120000000000000000

Offset: 0

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

• nonn

Crossrefs

Cf. A268506, A294319, A294321, A294323, A294325, A294326.

Programs

Mathematica

Table[Product[(5*k + 2)!, {k, 0, n}] , {n, 0, 10}]
FoldList[Times,(5Range[0,10]+2)!] (* Harvey P. Dale, Aug 11 2024 *)

Formula

a(n) ~ 2^(n/2 + 6/5) * 5^(5*n^2/2 + 5*n + 7/3) * n^(5*n^2/2 + 5*n + 137/60) * Pi^(n/2 + 11/10) / (A^(1/5) * (1 + sqrt(5))^(1/10) * Gamma(1/5)^(2/5) * Gamma(2/5)^(4/5) * exp(15*n^2/4 + 5*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).