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 A354393 #16 Feb 26 2023 12:54:54
%S A354393 1,0,0,0,-1,-10,-65,-350,-1631,-5250,18395,685850,10485739,127737610,
%T A354393 1336804105,11432407350,54280609109,-712071643930,-29671691715185,
%U A354393 -660215774400350,-11770593620859521,-176475952496559870,-2055362595355830475,-9749893741512339250
%N A354393 Expansion of e.g.f. 1/(1 + (exp(x) - 1)^4 / 24).
%F A354393 a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling2(k,4) * a(n-k).
%F A354393 a(n) = Sum_{k=0..floor(n/4)} (4*k)! * Stirling2(n,4*k)/(-24)^k.
%o A354393 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(exp(x)-1)^4/24)))
%o A354393 (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, 4, 2)*v[i-j+1])); v;
%o A354393 (PARI) a(n) = sum(k=0, n\4, (4*k)!*stirling(n, 4*k, 2)/(-24)^k);
%Y A354393 Cf. A354391, A354392, A354394.
%Y A354393 Cf. A346895, A354390, A354397.
%K A354393 sign
%O A354393 0,6
%A A354393 _Seiichi Manyama_, May 25 2022