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 A368166 #17 Jan 22 2025 06:39:12
%S A368166 0,0,0,0,4,10,40,210,1904,15120,132600,1293600,14673120,178738560,
%T A368166 2341182480,32915282400,499117301760,8075042976000,138689356915200,
%U A368166 2519863488979200,48354005826489600,976893364144857600,20721305503846886400,460363370406207206400
%N A368166 Expansion of e.g.f. -log(1 + x^3/6 * log(1 - x)).
%C A368166 This sequence is different from A351493.
%H A368166 Seiichi Manyama, <a href="/A368166/b368166.txt">Table of n, a(n) for n = 0..450</a>
%F A368166 a(n) = n! * Sum_{k=1..floor(n/4)} (k-1)! * |Stirling1(n-3*k,k)|/(6^k * (n-3*k)!).
%F A368166 a(0) = a(1) = a(2) = a(3) = 0; a(n) = n!/(6*(n-3)) + Sum_{k=4..n-1} k!/(6*(k-3)) * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Jan 22 2025
%o A368166 (PARI) a(n) = n!*sum(k=1, n\4, (k-1)!*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));
%Y A368166 Cf. A052804, A368165.
%Y A368166 Cf. A351493, A351506.
%K A368166 nonn
%O A368166 0,5
%A A368166 _Seiichi Manyama_, Dec 14 2023