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 A357617 #26 Oct 07 2022 15:47:03
%S A357617 0,1,4,17,88,657,6844,83393,1072880,14242785,197046964,2895895345,
%T A357617 45930435016,789930042865,14628150636012,287915593953889,
%U A357617 5950831121362656,128180962018224833,2868724306984850020,66704877850797014353,1613138176448134032440
%N A357617 Expansion of e.g.f. sinh( (exp(4*x) - 1)/4 ).
%F A357617 a(n) = Sum_{k=0..floor((n-1)/2)} 4^(n-1-2*k) * Stirling2(n,2*k+1).
%F A357617 a(n) ~ 2^(2*n-1) * exp(n/LambertW(4*n) - n - 1/4) * n^n / (LambertW(4*n)^n * sqrt(1 + LambertW(4*n))). - _Vaclav Kotesovec_, Oct 07 2022
%t A357617 With[{m = 20}, Range[0, m]! * CoefficientList[Series[Sinh[(Exp[4*x] - 1)/4], {x, 0, m}], x]] (* _Amiram Eldar_, Oct 07 2022 *)
%o A357617 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(4*x)-1)/4))))
%o A357617 (PARI) a(n) = sum(k=0, (n-1)\2, 4^(n-1-2*k)*stirling(n, 2*k+1, 2));
%Y A357617 Cf. A009599, A024429, A356572.
%Y A357617 Cf. A357650.
%K A357617 nonn
%O A357617 0,3
%A A357617 _Seiichi Manyama_, Oct 07 2022