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 A368165 #21 Jan 22 2025 06:39:19
%S A368165 0,0,0,3,6,20,180,1134,7980,78840,798840,8620920,107668440,1449377280,
%T A368165 20755871136,323448048000,5398086002400,95487623038080,
%U A368165 1796842848654720,35808112038746880,751616958775939200,16600116241063514880,384905905873078867200
%N A368165 Expansion of e.g.f. -log(1 + x^2/2 * log(1 - x)).
%H A368165 Seiichi Manyama, <a href="/A368165/b368165.txt">Table of n, a(n) for n = 0..444</a>
%F A368165 a(n) = n! * Sum_{k=1..floor(n/3)} (k-1)! * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).
%F A368165 a(0) = a(1) = a(2) = 0; a(n) = n!/(2*(n-2)) + Sum_{k=3..n-1} k!/(2*(k-2)) * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Jan 22 2025
%t A368165 With[{nn =30},CoefficientList[Series[-Log[1+x^2/2 Log[1-x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 22 2024 *)
%o A368165 (PARI) a(n) = n!*sum(k=1, n\3, (k-1)!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
%Y A368165 Cf. A052804, A368166.
%Y A368165 Cf. A351505.
%K A368165 nonn
%O A368165 0,4
%A A368165 _Seiichi Manyama_, Dec 14 2023