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 A353608 #11 May 08 2022 08:45:08
%S A353608 1,0,1,-4,21,-126,1023,-8240,84745,-864370,10925883,-133566808,
%T A353608 1994183205,-28455880012,489891177051,-8112780640000,158096182329585,
%U A353608 -2911196026492074,64115697136312563,-1328879415116924744,31920276313015362525,-728711636884140292372
%N A353608 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + sinh(x).
%t A353608 nn = 22; f[x_] := Product[(1 + a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Sinh[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y A353608 Cf. A006973, A137852, A353607, A353609, A353610, A353611.
%K A353608 sign
%O A353608 1,4
%A A353608 _Ilya Gutkovskiy_, May 07 2022