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 A354392 #10 May 25 2022 09:15:25
%S A354392 1,0,0,-1,-6,-25,-70,119,4354,48215,371610,1620839,-10665886,
%T A354392 -388969945,-6114636710,-65181228841,-325375497726,5950049261495,
%U A354392 226564100074970,4447402833379079,57902620204276834,258292327155958535,-12701483290229413350
%N A354392 Expansion of e.g.f. 1/(1 + (exp(x) - 1)^3 / 6).
%F A354392 a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling2(k,3) * a(n-k).
%F A354392 a(n) = Sum_{k=0..floor(n/3)} (3*k)! * Stirling2(n,3*k)/(-6)^k.
%o A354392 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(exp(x)-1)^3/6)))
%o A354392 (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, j)*stirling(j, 3, 2)*v[i-j+1])); v;
%o A354392 (PARI) a(n) = sum(k=0, n\3, (3*k)!*stirling(n, 3*k, 2)/(-6)^k);
%Y A354392 Cf. A354391, A354393, A354394.
%Y A354392 Cf. A346894, A346922.
%K A354392 sign
%O A354392 0,5
%A A354392 _Seiichi Manyama_, May 25 2022