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 A317747 #49 Sep 02 2018 08:22:09
%S A317747 1,-1,1,259193,-1036793,-201551328007,9137074752049,
%T A317747 9142431862033871923,-11105299580705049589,
%U A317747 -11003865617473929216508154207,114467620015003245418244743007,32505236416490926096399421788847363,-254505521478572052318535393350091231,-1828472168539763642032546635313363411876021
%N A317747 Numerator of the coefficient of z^(-n) in the Stirling-like asymptotic expansion of Product_{z=1..n} z^(z^2).
%C A317747 1^(1^2)*2^(2^2)*...*n^(n^2) ~ A_2*n^(n^3/3+n^2/2+n/6)*exp(-n^3/9+n/12)*(Sum_{k>=0} b(k)/n^k)^n, where A_2 is the second Bendersky constant.
%C A317747 a(n) is the numerator of b(n).
%H A317747 Seiichi Manyama, <a href="/A317747/b317747.txt">Table of n, a(n) for n = 0..174</a>
%H A317747 Weiping Wang, <a href="https://www.researchgate.net/publication/318153972_Some_asymptotic_expansions_on_hyperfactorial_functions_and_generalized_Glaisher-Kinkelin_constants">Some asymptotic expansions on hyperfactorial functions and generalized Glaisher-Kinkelin constants</a>, ResearchGate, 2017.
%F A317747 Let B_n be the Bernoulli number, and define the sequence {c_n} by the recurrence
%F A317747 c_0 = 1, c_n = (2/n) * Sum_{k=0..n-1} B_{n-k+3}*c_k/((n-j+1)*(n-k+2)*(n-k+3)) for n > 0.
%F A317747 a(n) is the numerator of c_n.
%e A317747 1^(1^2)*2^(2^2)*...*n^(n^2) ~ A_2*n^(n^3/3+n^2/2+n/6)*exp(-n^3/9+n/12)*(1 - 1/(360*n) + 1/(259200*n^2) + 259193/(1959552000*n^3) - 1036793/(2821754880000*n^4) - 201551328007/(5079158784000000*n^5) + ... ).
%Y A317747 Product_{z=1..n} z^(z^m): A001163/A001164 (m=0), A143475/A143476 (m=1), A317747/A317796 (m=2).
%Y A317747 Cf. A051675, A243262 (A_2).
%K A317747 sign,frac
%O A317747 0,4
%A A317747 _Seiichi Manyama_, Sep 01 2018