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 A368174 #16 Jan 22 2025 06:38:37
%S A368174 0,0,0,0,4,10,20,35,616,5124,29520,138765,1312300,16576846,175795984,
%T A368174 1539037955,15687832720,216382727240,3170822906976,42007311638169,
%U A368174 553841577209940,8435274815148370,145708900713412960,2517047758252082671,42575155321545439384
%N A368174 Expansion of e.g.f. -log(1 - x^3/6 * (exp(x) - 1)).
%C A368174 This sequence is different from A354001.
%H A368174 Seiichi Manyama, <a href="/A368174/b368174.txt">Table of n, a(n) for n = 0..471</a>
%F A368174 a(n) = n! * Sum_{k=1..floor(n/4)} (k-1)! * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).
%F A368174 a(0) = a(1) = a(2) = a(3) = 0; a(n) = binomial(n,3) + Sum_{k=4..n-1} binomial(k,3) * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Jan 22 2025
%o A368174 (PARI) a(n) = n!*sum(k=1, n\4, (k-1)!*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
%Y A368174 Cf. A052858, A368173.
%Y A368174 Cf. A353999, A354001.
%K A368174 nonn
%O A368174 0,5
%A A368174 _Seiichi Manyama_, Dec 14 2023