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 A302609 #15 Oct 05 2024 13:23:07
%S A302609 0,1,4,29,288,3649,56160,1017029,21181440,498682881,13095232000,
%T A302609 379443829709,12025239367680,413761766695809,15360425115176960,
%U A302609 611958601019294325,26042588632355176448,1179009749826940037889,56579126414696034729984,2868848293506101088635389
%N A302609 a(n) = n! * [x^n] exp(n*x)*arctanh(x).
%H A302609 Vaclav Kotesovec, <a href="/A302609/b302609.txt">Table of n, a(n) for n = 0..384</a>
%H A302609 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A302609 E.g.f.: log((1 - LambertW(-x))/(1 + LambertW(-x))) / (2*(1 + LambertW(-x))). - _Vaclav Kotesovec_, Jun 09 2019
%F A302609 a(n) ~ log(n) * n^n / 4 * (1 + (gamma + 3*log(2))/log(n)), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Jun 09 2019
%F A302609 a(n) = Sum_{k=1..n} binomial(n,k)*(k-1)!*n^(n-k)*(1-(-1)^k)/2. - _Fabian Pereyra_, Oct 05 2024
%t A302609 Table[n! SeriesCoefficient[Exp[n x] ArcTanh[x], {x, 0, n}], {n, 0, 19}]
%t A302609 nmax = 20; CoefficientList[Series[Log[(1 - LambertW[-x])/(1 + LambertW[-x])] / (2*(1 + LambertW[-x])), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Jun 09 2019 *)
%Y A302609 Cf. A010050, A291484, A293193, A302583, A302584, A302585, A302586, A302587, A302605, A302606, A302608.
%K A302609 nonn
%O A302609 0,3
%A A302609 _Ilya Gutkovskiy_, Apr 10 2018