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 A353999 #10 May 13 2022 12:05:58
%S A353999 1,0,0,0,4,10,20,35,1176,10164,58920,277365,3363580,47567806,
%T A353999 519759604,4591587455,51017687280,786120055400,12187597925136,
%U A353999 165128862881769,2261843835692340,36940778814100210,678763188831800380,12143893591131411571,211404290379223149384
%N A353999 Expansion of e.g.f. 1/(1 - x^3/6 * (exp(x) - 1)).
%F A353999 a(0) = 1; a(n) = n!/6 * Sum_{k=4..n} 1/(k-3)! * a(n-k)/(n-k)! = binomial(n,3) * Sum_{k=4..n} binomial(n-3,k-3) * a(n-k).
%F A353999 a(n) = n! * Sum_{k=0..floor(n/4)} k! * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).
%o A353999 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3/6*(exp(x)-1))))
%o A353999 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!/6*sum(j=4, i, 1/(j-3)!*v[i-j+1]/(i-j)!)); v;
%o A353999 (PARI) a(n) = n!*sum(k=0, n\4, k!*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
%Y A353999 Cf. A052848, A353998.
%Y A353999 Cf. A000292, A351506, A354001.
%K A353999 nonn
%O A353999 0,5
%A A353999 _Seiichi Manyama_, May 13 2022