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 A353912 #6 May 11 2022 10:37:21
%S A353912 1,-2,-2,-16,-24,64,-720,-23808,-35840,282368,-3628800,-75458560,
%T A353912 -479001600,5315078144,-82614884352,-8601835798528,-20922789888000,
%U A353912 321288633450496,-6402373705728000,-309168395474436096,-2379913632645120000,46441359567137275904
%N A353912 Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + tanh(x).
%t A353912 nn = 22; f[x_] := Product[1/(1 - a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Tanh[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y A353912 Cf. A155585, A353779, A353873, A353910, A353911.
%K A353912 sign
%O A353912 1,2
%A A353912 _Ilya Gutkovskiy_, May 10 2022