A268506 a(n) = Product_{k=0..n} (5*k)!.

1, 120, 435456000, 569434649591808000000, 1385378702517271000054360965120000000000, 21488900044302744250061179567064173417691432878080000000000000000

Offset: 0

Author

Vaclav Kotesovec, Apr 16 2016

Keywords

• nonn

Comments

Partial products of A100734. - Michel Marcus, Jul 06 2019

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..16

Crossrefs

Cf. A000178, A098694, A100734, A268504, A268505, A271946, A271947.

Programs

Mathematica

Table[Product[(5*k)!,{k,0,n}],{n,0,8}]

PARI

{a(n) = prod(k=1, n, (5*k)!)} \\ Seiichi Manyama, Jul 06 2019

Formula

a(n) ~ Gamma(1/5)^(3/5) * Gamma(2/5)^(2/5) * Gamma(3/5)^(1/5) * 2^(n/2 - 1/10) * Pi^(n/2 - 1/10) * 5^(23/60 + 3*n + 5*n^2/2) * exp(1/60 - 3*n - 15*n^2/4) * n^(41/60 + 3*n + 5*n^2/2) / A^(1/5), where A = A074962 is the Glaisher-Kinkelin constant.