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 A350726 #16 Feb 04 2022 08:23:23
%S A350726 1,1,0,-3,21,-100,-525,33026,-860503,16304464,-100885935,-12798492630,
%T A350726 1037135603845,-55556702499792,2207903148318777,-31916679640973750,
%U A350726 -6164889702150516015,983802138243128355456,-100629406324320358067423
%N A350726 a(n) = Sum_{k=0..n} k^(n-k) * Stirling1(n,k).
%F A350726 E.g.f.: Sum_{k>=0} log(1 + k*x)^k / (k! * k^k).
%t A350726 a[0] = 1; a[n_] := Sum[k^(n - k) * StirlingS1[n, k], {k, 1, n}]; Array[a, 19, 0] (* _Amiram Eldar_, Feb 03 2022 *)
%o A350726 (PARI) a(n) = sum(k=0, n, k^(n-k)*stirling(n, k, 1));
%o A350726 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k*x)^k/(k!*k^k))))
%Y A350726 Cf. A229233, A305819, A320082, A350725.
%K A350726 sign
%O A350726 0,4
%A A350726 _Seiichi Manyama_, Feb 03 2022