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 A385500 #13 Jul 01 2025 08:48:54
%S A385500 1,1,3,18,149,1640,22359,366128,6998697,153191808,3779353515,
%T A385500 103800229632,3141633970749,103904351855616,3728602377979647,
%U A385500 144297781732300800,5991021498320041809,265636734347975688192,12527923794824003280723,626224876080360687599616
%N A385500 Expansion of e.g.f. exp( -LambertW(-arctanh(x)) ).
%H A385500 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A385500 E.g.f. A(x) satisfies A(x) = exp( arctanh(x) * A(x) ).
%F A385500 E.g.f. A(x) satisfies A(x) = ( (1+x)/(1-x) )^(A(x)/2).
%F A385500 a(n) = Sum_{k=0..n} (k+1)^(k-1) * A111594(n,k).
%F A385500 a(n) ~ sqrt(exp(4*exp(-1)) - 1) * n^(n-1) / (2*exp(n - 3/2 + exp(-1)) * tanh(exp(-1))^n). - _Vaclav Kotesovec_, Jul 01 2025
%t A385500 nmax=19; CoefficientList[Series[Exp[ -LambertW[-ArcTanh[x]]],{x,0,nmax}],x]Range[0,nmax]! (* _Stefano Spezia_, Jul 01 2025 *)
%o A385500 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-atanh(x)))))
%Y A385500 Cf. A385501, A385502.
%Y A385500 Cf. A111594, A385425.
%K A385500 nonn
%O A385500 0,3
%A A385500 _Seiichi Manyama_, Jul 01 2025