cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A268506 #18 Jul 06 2019 04:11:42
%S A268506 1,120,435456000,569434649591808000000,
%T A268506 1385378702517271000054360965120000000000,
%U A268506 21488900044302744250061179567064173417691432878080000000000000000
%N A268506 a(n) = Product_{k=0..n} (5*k)!.
%C A268506 Partial products of A100734. - _Michel Marcus_, Jul 06 2019
%H A268506 Seiichi Manyama, <a href="/A268506/b268506.txt">Table of n, a(n) for n = 0..16</a>
%F A268506 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 A268506 Table[Product[(5*k)!,{k,0,n}],{n,0,8}]
%o A268506 (PARI) {a(n) = prod(k=1, n, (5*k)!)} \\ _Seiichi Manyama_, Jul 06 2019
%Y A268506 Cf. A000178, A098694, A100734, A268504, A268505, A271946, A271947.
%K A268506 nonn
%O A268506 0,2
%A A268506 _Vaclav Kotesovec_, Apr 16 2016