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 A356572 #33 Oct 07 2022 15:47:07
%S A356572 0,1,3,10,45,307,2718,26371,265359,2778976,30916863,372113623,
%T A356572 4873075056,68908186765,1037694932823,16438615126282,271972422548361,
%U A356572 4687666317874495,84181305836224422,1576083180118379527,30757003280682603699,624671260245315540568
%N A356572 Expansion of e.g.f. sinh( (exp(3*x) - 1)/3 ).
%F A356572 a(n) = Sum_{k=0..floor((n-1)/2)} 3^(n-1-2*k) * Stirling2(n,2*k+1).
%F A356572 a(n) ~ 3^n * exp(n/LambertW(3*n) - n - 1/3) * n^n / (LambertW(3*n)^n * 2*sqrt(1 + LambertW(3*n))). - _Vaclav Kotesovec_, Oct 07 2022
%t A356572 With[{m = 20}, Range[0, m]! * CoefficientList[Series[Sinh[(Exp[3*x] - 1)/3], {x, 0, m}], x]] (* _Amiram Eldar_, Oct 07 2022 *)
%o A356572 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(3*x)-1)/3))))
%o A356572 (PARI) a(n) = sum(k=0, (n-1)\2, 3^(n-1-2*k)*stirling(n, 2*k+1, 2));
%Y A356572 Cf. A009599, A024429, A357617.
%Y A356572 Cf. A357649.
%K A356572 nonn
%O A356572 0,3
%A A356572 _Seiichi Manyama_, Oct 07 2022