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 A375688 #13 Aug 25 2024 09:57:51
%S A375688 1,0,2,3,56,270,4824,44520,866816,12195792,267873120,5073187680,
%T A375688 126754229568,2999710359360,85061489235072,2400155295632640,
%U A375688 76724104598031360,2502434971473937920,89428428468644493312,3300036525511418327040
%N A375688 Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(1/3).
%F A375688 a(n) = n! * Sum_{k=0..floor(n/2)} (Product_{j=0..k-1} (3*j+1)) * |Stirling1(n-k,k)|/(n-k)!.
%o A375688 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*log(1-x))^(1/3)))
%o A375688 (PARI) a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+1)*abs(stirling(n-k, k, 1))/(n-k)!);
%Y A375688 Cf. A367879, A375689.
%Y A375688 Cf. A347015.
%K A375688 nonn
%O A375688 0,3
%A A375688 _Seiichi Manyama_, Aug 24 2024