A119029 Numerator of Sum_{k=1..n} n^(k-1)/k!.

1, 2, 4, 25, 217, 203, 6743, 69511, 1184417, 728102, 5720654791, 601499, 4670663321629, 42568060798, 888330615353, 15438515749903, 1676770323947695709, 30538296012677, 16858207434636875406943

Offset: 1

Author

Alexander Adamchuk, Jul 22 2006

Keywords

• frac
• nonn

Comments

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

Examples

			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
		

Crossrefs

Cf. A063170, A090878, A093101, A120266, A120267, A214401 (denominators), A214402.

Programs

Mathematica

Numerator[Table[Sum[n^(k-1)/k!,{k,1,n}],{n,1,30}]]

Formula

a(n) = numerator(Sum_{k=1..n} n^(k-1)/k!).

a(n) = A120267(n)/n.