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 A377376 #55 Jan 23 2025 08:31:31
%S A377376 0,0,0,1,6,35,215,1414,9912,73324,565170,4472226,35725426,283350132,
%T A377376 2225790476,18624038224,216679183120,4293834561200,111300845967440,
%U A377376 2963219043255360,76258914698507280,1895550595605889760,45928558583373219600,1093984400513512753840
%N A377376 Expansion of e.g.f. log( 1 - log(1 - x)^3 / 6 ).
%F A377376 a(n) = Sum_{k=1..floor(n/3)} (-1)^(k-1) * (3*k)! * |Stirling1(n,3*k)|/(k * 6^k).
%F A377376 a(n) = |Stirling1(n,3)| - Sum_{k=1..n-1} |Stirling1(k,3)| * binomial(n-1,k) * a(n-k).
%o A377376 (PARI) a(n) = sum(k=1, n\3, (-1)^(k-1)*(3*k)!*abs(stirling(n, 3*k, 1))/(k*6^k));
%Y A377376 Cf. A346966, A379674, A380370.
%K A377376 nonn
%O A377376 0,5
%A A377376 _Seiichi Manyama_, Jan 23 2025