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 A296838 #7 Dec 21 2017 17:38:18
%S A296838 0,1,-4,48,-1186,50060,-3226206,294835184,-36270477034,5779302944436,
%T A296838 -1157856177719830,284876691727454552,-84442374415240892898,
%U A296838 29680054107768128647388,-12205478262363331593956686,5805823539844285054558025280,-3163004294186696659107788567386
%N A296838 Expansion of e.g.f. log(1 + x*tanh(x/2)) (even powers only).
%H A296838 Vaclav Kotesovec, <a href="/A296838/b296838.txt">Table of n, a(n) for n = 0..200</a>
%F A296838 a(n) = (2*n)! * [x^(2*n)] log(1 + x*tanh(x/2)).
%F A296838 a(n) ~ -(-1)^n * sqrt(Pi) * 2^(2*n + 1) * n^(2*n - 1/2) / (r^(2*n) * exp(2*n)), where r = 1.306542374188806202228727831923118284841279755635... is the root of the equation r * tan(r/2) = 1. - _Vaclav Kotesovec_, Dec 21 2017
%e A296838 log(1 + x*tanh(x/2)) = x^2/2! - 4*x^4/4! + 48*x^6/6! - 1186*x^8/8! + ...
%t A296838 nmax = 16; Table[(CoefficientList[Series[Log[1 + x Tanh[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
%Y A296838 Cf. A001469, A003707, A009379, A009399, A110501, A296837.
%K A296838 sign
%O A296838 0,3
%A A296838 _Ilya Gutkovskiy_, Dec 21 2017