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 A331798 #8 Jan 26 2020 17:48:31
%S A331798 0,1,5,29,204,1714,16862,190826,2447512,35136696,558727872,9754239648,
%T A331798 185546362416,3820734689472,84687887312688,2010622152615504,
%U A331798 50908186083448320,1369376758488222336,38998680958184088960,1172297572938013827456,37092793335394301708544
%N A331798 E.g.f.: -log(1 - x) / ((1 - x) * (1 + log(1 - x))).
%F A331798 a(n) = Sum_{k=0..n} = |Stirling1(n,k)| * A007526(k).
%F A331798 a(n) = Sum_{k=1..n} binomial(n,k) * k! * H(k) * A007840(n-k), where H(k) is the k-th harmonic number.
%F A331798 a(n) ~ n! / (1 - exp(-1))^(n+1). - _Vaclav Kotesovec_, Jan 26 2020
%t A331798 nmax = 20; CoefficientList[Series[-Log[1 - x]/((1 - x) (1 + Log[1 - x])), {x, 0, nmax}], x] Range[0, nmax]!
%t A331798 A007526[n_] := n! Sum[1/k!, {k, 0, n - 1}]; a[n_] := Sum[Abs[StirlingS1[n, k]] A007526[k], {k, 0, n}]; Table[a[n], {n, 0, 20}]
%t A331798 A007840[n_] := Sum[Abs[StirlingS1[n, k]] k!, {k, 0, n}]; a[n_] := Sum[Binomial[n, k] k! HarmonicNumber[k] A007840[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%Y A331798 Cf. A000254, A001008, A002805, A003713, A007526, A007840, A215916, A331797.
%K A331798 nonn
%O A331798 0,3
%A A331798 _Ilya Gutkovskiy_, Jan 26 2020