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%I #13 May 12 2020 16:25:37
%S 1,2,4,25,217,203,6743,69511,1184417,728102,5720654791,601499,
%T 4670663321629,42568060798,888330615353,15438515749903,
%U 1676770323947695709,30538296012677,16858207434636875406943
%N Numerator of Sum_{k=1..n} n^(k-1)/k!.
%C 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 a(n) = numerator(Sum_{k=1..n} n^(k-1)/k!).
%F a(n) = A120267(n)/n.
%e 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 Numerator[Table[Sum[n^(k-1)/k!,{k,1,n}],{n,1,30}]]
%Y Cf. A063170, A090878, A093101, A120266, A120267, A214401 (denominators), A214402.
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, Jul 22 2006
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