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 A350725 #15 Feb 04 2022 08:23:17
%S A350725 1,1,1,-4,-2,274,-3442,-12552,2108664,-63083232,87416112,112192496976,
%T A350725 -7487840132544,174521224997040,19793498724358032,
%U A350725 -3109195219736188416,209306170972547346816,2973238556525799866496,-3013574861684426837113728,456220653756733889826621696
%N A350725 a(n) = Sum_{k=0..n} k! * k^(n-k) * Stirling1(n,k).
%F A350725 E.g.f.: Sum_{k>=0} log(1 + k*x)^k / k^k.
%t A350725 a[0] = 1; a[n_] := Sum[k! * k^(n-k) * StirlingS1[n, k], {k, 1, n}]; Array[a, 20, 0] (* _Amiram Eldar_, Feb 03 2022 *)
%o A350725 (PARI) a(n) = sum(k=0, n, k!*k^(n-k)*stirling(n, k, 1));
%o A350725 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k*x)^k/k^k)))
%Y A350725 Cf. A007840, A229234, A320083, A350721, A350726.
%K A350725 sign
%O A350725 0,4
%A A350725 _Seiichi Manyama_, Feb 03 2022