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 A128044 #13 Sep 01 2021 22:21:25
%S A128044 1,1,5,35,27,156,25951,419681,646379,13439609,5544403,56359019,
%T A128044 109370096651,218981057573,1073115579569,334684898286103,
%U A128044 8505202310547841,515483074900523,712333151156230489
%N A128044 a(n) = numerator of b(n), where b(1) = 1, b(n) = Sum_{k=1..n-1} b(n-k) * H(k); H(k) = Sum_{j=1..k} 1/j, the k-th harmonic number.
%F A128044 G.f. for fractions: x / (1 + log(1 - x) / (1 - x)). - _Ilya Gutkovskiy_, Sep 01 2021
%e A128044 1, 1, 5/2, 35/6, 27/2, 156/5, 25951/360, 419681/2520, 646379/1680, 13439609/15120, 5544403/2700, 56359019/11880, ...
%t A128044 f[l_List] := Block[{n = Length[l] + 1},Append[l, Sum[l[[n - k]]*HarmonicNumber[k], {k, n - 1}]]];Numerator[Nest[f, {1}, 20]] (* _Ray Chandler_, Feb 12 2007 *)
%Y A128044 Cf. A001008, A002805, A128045 (denominators), A305306.
%K A128044 nonn,frac
%O A128044 1,3
%A A128044 _Leroy Quet_, Feb 11 2007
%E A128044 Extended by _Ray Chandler_, Feb 12 2007