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 A354686 #5 Jun 03 2022 07:41:00
%S A354686 0,1,1,-4,38,-646,17124,-651120,33563760,-2251415376,190506294720,
%T A354686 -19843054116480,2494435702953600,-372324067662349440,
%U A354686 65089674982557308160,-13172994619821785548800,3055455516855073351219200,-805168341051328705189939200
%N A354686 a(n) = n! * Sum_{k=1..n} Stirling1(n,k) * H(k), where H(k) is the k-th harmonic number.
%F A354686 Sum_{n>=0} a(n) * x^n / n!^2 = Sum_{n>=1} H(n) * log(1+x)^n / n!.
%t A354686 Table[n! Sum[StirlingS1[n, k] HarmonicNumber[k], {k, 1, n}], {n, 0, 17}]
%t A354686 nmax = 17; CoefficientList[Series[Sum[HarmonicNumber[k] Log[1 + x]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^2
%Y A354686 Cf. A001008, A002805, A087751, A222059, A302547, A354685.
%K A354686 sign
%O A354686 0,4
%A A354686 _Ilya Gutkovskiy_, Jun 03 2022