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 A375685 #10 Sep 01 2024 10:13:16
%S A375685 1,0,0,6,12,40,720,4788,34440,460080,5246640,60318720,879523920,
%T A375685 13298126400,206628117696,3575354428800,65828785276800,
%U A375685 1264510188264960,25912058505776640,561351949518931200,12721171715573529600,302794615563937781760,7554095183751745305600
%N A375685 Expansion of e.g.f. 1 / (1 + x^2/2 * log(1 - x))^2.
%F A375685 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A351505.
%F A375685 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)! * |Stirling1(n-2*k,k)|/(2^k*(n-2*k)!).
%o A375685 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^2/2*log(1-x))^2))
%o A375685 (PARI) a(n) = n!*sum(k=0, n\3, (k+1)!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
%Y A375685 Cf. A351505, A375686.
%Y A375685 Cf. A375237.
%K A375685 nonn
%O A375685 0,4
%A A375685 _Seiichi Manyama_, Aug 24 2024