A271946 a(n) = Product_{k=0..n} (6*k)!.

1, 720, 344881152000, 2208058019165981638656000000, 1369986068925795885347091500568179543900160000000000, 363392722685428853076589064611759104109572860599125858715484081356800000000000000000

Offset: 0

Author

Vaclav Kotesovec, Apr 17 2016

Keywords

• nonn

Comments

The next term has 126 digits.

Partial products of A195390. - Michel Marcus, Jul 06 2019

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..15

Crossrefs

Cf. A000178, A098694, A195390, A268504, A268505, A268506, A271947.

Programs

Mathematica

Table[Product[(6*k)!,{k,0,n}],{n,0,8}]

PARI

{a(n) = prod(k=1, n, (6*k)!)} \\ Seiichi Manyama, Jul 06 2019

Formula

a(n) ~ A^(-1/6) * exp(1/72 - 7*n/2 - 9*n^2/2) * n^(55/72 + 7*n/2 + 3*n^2) * 2^(1/72 + 4*n + 3*n^2) * 3^(47/72 + 7*n/2 + 3*n^2) * Pi^(n/2 - 1/3) * Gamma(1/3)^(5/3), where A = A074962 is the Glaisher-Kinkelin constant.