login
a(n) = Product_{k=0..n} (6*k)!.
10

%I #16 Jul 06 2019 05:38:30

%S 1,720,344881152000,2208058019165981638656000000,

%T 1369986068925795885347091500568179543900160000000000,

%U 363392722685428853076589064611759104109572860599125858715484081356800000000000000000

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

%C The next term has 126 digits.

%C Partial products of A195390. - _Michel Marcus_, Jul 06 2019

%H Seiichi Manyama, <a href="/A271946/b271946.txt">Table of n, a(n) for n = 0..15</a>

%F 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.

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

%o (PARI) {a(n) = prod(k=1, n, (6*k)!)} \\ _Seiichi Manyama_, Jul 06 2019

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

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Apr 17 2016