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 A375689 #14 Aug 25 2024 09:57:55
%S A375689 1,0,4,6,136,660,13188,123480,2584160,37044000,855658800,16536548160,
%T A375689 428924382720,10358056051200,302474317729920,8701780305254400,
%U A375689 284949736641177600,9464366170599782400,345224605512559518720,12956112412535827353600
%N A375689 Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(2/3).
%F A375689 a(n) = n! * Sum_{k=0..floor(n/2)} (Product_{j=0..k-1} (3*j+2)) * |Stirling1(n-k,k)|/(n-k)!.
%o A375689 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*log(1-x))^(2/3)))
%o A375689 (PARI) a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+2)*abs(stirling(n-k, k, 1))/(n-k)!);
%Y A375689 Cf. A367879, A375688.
%Y A375689 Cf. A365575.
%K A375689 nonn
%O A375689 0,3
%A A375689 _Seiichi Manyama_, Aug 24 2024