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 A354396 #13 Dec 02 2023 11:58:54
%S A354396 1,0,0,-1,-6,-25,-80,-91,1694,23155,206340,1442969,6928394,-6507865,
%T A354396 -752409840,-12953182971,-160186016906,-1548849362085,-9789241693220,
%U A354396 28359195353489,2378650585685794,52832659521004495,855581150441210600,10878338100191146749
%N A354396 Expansion of e.g.f. exp( -(exp(x) - 1)^3 / 6 ).
%F A354396 a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n-1,k-1) * Stirling2(k,3) * a(n-k).
%F A354396 a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling2(n,3*k)/((-6)^k * k!).
%t A354396 With[{nn=30},CoefficientList[Series[Exp[-(Exp[x]-1)^3/6],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 02 2023 *)
%o A354396 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-(exp(x)-1)^3/6)))
%o A354396 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i-1, j-1)*stirling(j, 3, 2)*v[i-j+1])); v;
%o A354396 (PARI) a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 2)/((-6)^k*k!));
%Y A354396 Cf. A000587, A354395, A354397, A354398.
%Y A354396 Cf. A327504, A354392.
%K A354396 sign
%O A354396 0,5
%A A354396 _Seiichi Manyama_, May 25 2022