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 A353880 #13 May 09 2022 15:19:06 %S A353880 1,0,0,0,6,30,165,1050,10192,108864,1230660,14758920,195861996, %T A353880 2852815680,44880446520,753211040400,13458760362720,255688784416800, %U A353880 5149255813778160,109489194918180000,2450182706364430080,57567025900160259840,1417073899136197468320 %N A353880 Expansion of e.g.f. 1/(1 - (x * log(1-x))^2 / 4). %F A353880 a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * |Stirling1(n-2*k,2*k)|/(4^k * (n-2*k)!). %o A353880 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*log(1-x))^2/4))) %o A353880 (PARI) a(n) = n!*sum(k=0, n\4, (2*k)!*abs(stirling(n-2*k, 2*k, 1))/(4^k*(n-2*k)!)); %Y A353880 Cf. A052830, A353881, A353882. %Y A353880 Cf. A346921, A353883. %K A353880 nonn %O A353880 0,5 %A A353880 _Seiichi Manyama_, May 09 2022