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 A119029 #13 May 12 2020 16:25:37
%S A119029 1,2,4,25,217,203,6743,69511,1184417,728102,5720654791,601499,
%T A119029 4670663321629,42568060798,888330615353,15438515749903,
%U A119029 1676770323947695709,30538296012677,16858207434636875406943
%N A119029 Numerator of Sum_{k=1..n} n^(k-1)/k!.
%C A119029 Apparently, the three sequences T_1(n) = Sum_{k=1..n} n^(k-1)/k!, T_2(n) = Sum_{k=0..n} n^k/k!, and T_3(n) = Sum_{k=1..n} n^k/k!, with numerators in A119029, A120266, and A120267, respectively, have the same denominators, listed in A214401. This, however, is not immediately obvious. - _Petros Hadjicostas_, May 12 2020
%F A119029 a(n) = numerator(Sum_{k=1..n} n^(k-1)/k!).
%F A119029 a(n) = A120267(n)/n.
%e A119029 The first few fractions are 1, 2, 4, 25/3, 217/12, 203/5, 6743/72, 69511/315, 1184417/2240, 728102/567, ... = A119029/A214401. - _Petros Hadjicostas_, May 12 2020
%t A119029 Numerator[Table[Sum[n^(k-1)/k!,{k,1,n}],{n,1,30}]]
%Y A119029 Cf. A063170, A090878, A093101, A120266, A120267, A214401 (denominators), A214402.
%K A119029 frac,nonn
%O A119029 1,2
%A A119029 _Alexander Adamchuk_, Jul 22 2006