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 A351506 #26 May 12 2022 12:15:56
%S A351506 1,0,0,0,4,10,40,210,2464,20160,178800,1755600,21215040,268107840,
%T A351506 3596916960,51452200800,800489733120,13262804755200,232536822336000,
%U A351506 4300843392518400,84023034413644800,1727339274045504000,37248117171719731200,840387048760633651200
%N A351506 Expansion of e.g.f. 1/(1 + x^3/6 * log(1 - x)).
%H A351506 Seiichi Manyama, <a href="/A351506/b351506.txt">Table of n, a(n) for n = 0..450</a>
%F A351506 a(0) = 1; a(n) = n!/6 * Sum_{k=4..n} 1/(k-3) * a(n-k)/(n-k)!.
%F A351506 a(n) = n! * Sum_{k=0..floor(n/4)} k! * |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).
%o A351506 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^3/6*log(1-x))))
%o A351506 (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 A351506 (PARI) a(n) = n!*sum(k=0, n\4, k!*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));
%Y A351506 Cf. A052830, A351505.
%Y A351506 Cf. A351493, A351504,
%K A351506 nonn
%O A351506 0,5
%A A351506 _Seiichi Manyama_, May 04 2022