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 A373873 #12 Jul 13 2025 15:12:48
%S A373873 0,1,3,31,765,34651,2502213,263824891,38248036725,7298877611371,
%T A373873 1773652375115973,534749297993098651,195883403209280580885,
%U A373873 85687658454617655817291,44120264185381411695106533,26413555571018242181844978811
%N A373873 a(n) = Sum_{k=1..n} k! * k^(n-2) * Stirling2(n,k).
%F A373873 E.g.f.: Sum_{k>=1} (exp(k*x) - 1)^k / k^2.
%t A373873 Table[Sum[k! k^(n-2) StirlingS2[n,k],{k,n}],{n,0,20}] (* _Harvey P. Dale_, Jul 13 2025 *)
%o A373873 (PARI) a(n) = sum(k=1, n, k!*k^(n-2)*stirling(n, k, 2));
%Y A373873 Cf. A122399, A244585, A373871.
%Y A373873 Cf. A220181, A373874, A373875.
%K A373873 nonn
%O A373873 0,3
%A A373873 _Seiichi Manyama_, Jun 20 2024