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 A381024 #13 Feb 12 2025 16:47:20
%S A381024 0,0,1,9,65,470,3634,30681,284066,2878284,31777851,380396665,
%T A381024 4912874691,68142259874,1010736134108,15970709345353,267890182932228,
%U A381024 4755088551397016,89059375695649173,1755426336571939497,36327033843657558661,787539492771039394158,17850021806783323801766
%N A381024 Expansion of e.g.f. log(1-x)^2 * exp(x) / (2 * (1-x)).
%F A381024 a(n) = Sum_{k=0..n} binomial(n,k) * |Stirling1(k+1,3)|.
%F A381024 a(n) = A381022(n+1) - A381022(n).
%t A381024 nmax=22;CoefficientList[Series[Log[1-x]^2* Exp[x]/ (2* (1-x)),{x,0,nmax}],x]Range[0,nmax]! (* _Stefano Spezia_, Feb 12 2025 *)
%o A381024 (PARI) a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(k+1, 3, 1)));
%Y A381024 Column k=3 of A269951 (with a different offset).
%Y A381024 Cf. A381022.
%K A381024 nonn
%O A381024 0,4
%A A381024 _Seiichi Manyama_, Feb 12 2025