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.
%I A317660 #52 Feb 16 2025 08:33:56
%S A317660 1,1,1,720,1,5040,1036800,10080,3628800,24634368000,6350400,
%T A317660 747242496000,3476402012160000,105670656000,11298306539520000,
%U A317660 1489290622009344000000,2259661307904000,6688268793387417600000,920024174652492349440000000,8655406673795481600000
%N A317660 Denominator of the coefficient of z^(-n) of asymptotic expansions related to hyperfactorial function H(z).
%C A317660 1^1*2^2*...*n^n ~ A*n^(n^2/2 + n/2 + 1/12)*exp(-n^2/4)*(Sum_{k>=0} b(k)/n^k)^n, where A is the Glaisher-Kinkelin constant.
%C A317660 a(n) is the denominator of b(n).
%H A317660 Seiichi Manyama, <a href="/A317660/b317660.txt">Table of n, a(n) for n = 0..362</a>
%H A317660 Chao-Ping Chen, <a href="https://doi.org/10.1016/j.jnt.2013.08.007">Asymptotic expansions for Barnes G-function</a>, Journal of Number Theory 135 (2014) 36-42.
%H A317660 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Hyperfactorial.html">Hyperfactorial</a>
%F A317660 Let B_n be the Bernoulli number, and define the sequence {c_n} by the recurrence
%F A317660 c_0 = 1, c_n = (-1/n) * Sum_{k=0..n-2} B_{n-k+1}*c_k/((n-k-1)*(n-k+1)) for n > 0.
%F A317660 a(n) is the denominator of c_n.
%e A317660 1^1*2^2*...*n^n ~ A*n^(n^2/2 + n/2 + 1/12)*exp(-n^2/4)*(1 + 1/(720*n^3) - 1/(5040*n^5) + 1/(1036800*n^6) + 1/(10080*n^7) - 1/(3628800*n^8) - 2591989/(24634368000*n^9) + ... )^n.
%Y A317660 Cf. A143476, A317615.
%K A317660 nonn,frac
%O A317660 0,4
%A A317660 _Seiichi Manyama_, Sep 01 2018