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 A354122 #16 Nov 19 2023 08:22:10
%S A354122 1,3,15,102,870,8892,105708,1431168,21722136,365105928,6729341832,
%T A354122 134915992560,2922576142320,68013701197920,1692075061072800,
%U A354122 44810389419079680,1258472984174461440,37357062009383877120,1168635883239630120960,38424619272539153157120
%N A354122 Expansion of e.g.f. 1/(1 + log(1 - x))^3.
%F A354122 a(n) = (1/2) * Sum_{k=0..n} (k + 2)! * |Stirling1(n,k)|.
%F A354122 a(n) ~ sqrt(Pi/2) * n^(n + 5/2) / (exp(1) - 1)^(n+3). - _Vaclav Kotesovec_, Jun 04 2022
%F A354122 a(0) = 1; a(n) = Sum_{k=1..n} (2*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Nov 19 2023
%o A354122 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x))^3))
%o A354122 (PARI) a(n) = sum(k=0, n, (k+2)!*abs(stirling(n, k, 1)))/2;
%Y A354122 Cf. A007840, A052801, A354123.
%Y A354122 Cf. A226515, A354120.
%K A354122 nonn
%O A354122 0,2
%A A354122 _Seiichi Manyama_, May 17 2022