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.

A365266 a(n) = Product_{k=1..n} Gamma(6*k).

This page as a plain text file.
%I A365266 #15 Sep 01 2023 04:07:49
%S A365266 1,120,4790016000,1703748471578689536000000,
%T A365266 44045334006101976766560297729172439040000000000,
%U A365266 389438360216723307909581902233109465138002465491175688781168640000000000000000
%N A365266 a(n) = Product_{k=1..n} Gamma(6*k).
%F A365266 a(n) = A^(35/6) * exp(-35/72) * Gamma(1/3)^(5/3) * 2^(-125/72 + 3*n^2) * 3^(47/72 + 5*n/2 + 3*n^2) * Pi^(-25/12 - 5*n/2) * BarnesG(1 + n) * BarnesG(7/6 + n) * BarnesG(4/3 + n) * BarnesG(3/2 + n) * BarnesG(5/3 + n) * BarnesG(11/6 + n), where A = A074962 is the Glaisher-Kinkelin constant.
%F A365266 a(n) ~ A^(-1/6) * Gamma(1/3)^(5/3) * 2^(-35/72 + 3*n + 3*n^2) * 3^(47/72 + 5*n/2 + 3*n^2) * exp(1/72 - 5*n/2 - 9*n^2/2) * n^(19/72 + 5*n/2 + 3*n^2) * Pi^(-5/6 + n/2), where A = A074962 is the Glaisher-Kinkelin constant.
%t A365266 Table[Product[Gamma[6*k], {k, 1, n}], {n, 0, 10}]
%t A365266 Table[Product[(6*k-1)!, {k, 1, n}], {n, 0, 10}]
%Y A365266 Cf. A000178, A168467, A294319, A294322, A294326.
%Y A365266 Cf. A055462, A306635, A306651.
%K A365266 nonn
%O A365266 0,2
%A A365266 _Vaclav Kotesovec_, Sep 01 2023