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a(n) = Product_{k=0..n} (5*k)!.
14

%I #18 Jul 06 2019 04:11:42

%S 1,120,435456000,569434649591808000000,

%T 1385378702517271000054360965120000000000,

%U 21488900044302744250061179567064173417691432878080000000000000000

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

%C Partial products of A100734. - _Michel Marcus_, Jul 06 2019

%H Seiichi Manyama, <a href="/A268506/b268506.txt">Table of n, a(n) for n = 0..16</a>

%F 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.

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

%o (PARI) {a(n) = prod(k=1, n, (5*k)!)} \\ _Seiichi Manyama_, Jul 06 2019

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

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Apr 16 2016