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 A351180 #17 Feb 19 2022 04:45:52
%S A351180 1,1,15,635,53112,7367444,1529130770,443685287576,171495189203456,
%T A351180 85174828026304824,52856314387144232184,40077340463437963801752,
%U A351180 36457068309928364981668848,39186634107857517367884040632
%N A351180 a(n) = Sum_{k=0..n} k^(k+n) * Stirling1(n,k).
%F A351180 E.g.f.: Sum_{k>=0} (k * log(1 + k*x))^k / k!.
%F A351180 a(n) ~ c * d^n * n^(2*n), where d = 0.9315722818790917570256960813246568629715677803436281996798798428122211769... and c = 1.07238575181275524934156216072811545518508724720534339814911465361... - _Vaclav Kotesovec_, Feb 18 2022
%t A351180 a[0] = 1; a[n_] := Sum[k^(k + n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 14, 0] (* _Amiram Eldar_, Feb 04 2022 *)
%o A351180 (PARI) a(n) = sum(k=0, n, k^(k+n)*stirling(n, k, 1));
%o A351180 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*log(1+k*x))^k/k!)))
%Y A351180 Cf. A305819, A320082, A350726, A351182, A351183.
%Y A351180 Cf. A350721, A351181, A351769.
%K A351180 nonn
%O A351180 0,3
%A A351180 _Seiichi Manyama_, Feb 04 2022