A120266 Numerator of Sum_{k=0..n} n^k/k!.

2, 5, 13, 103, 1097, 1223, 47273, 556403, 10661993, 7281587, 62929017101, 7218065, 60718862681977, 595953719897, 13324966405463, 247016301114823, 28505097599389815853, 549689343118061, 320305944459287485595917

Offset

1,1

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

Links

Table of n, a(n) for n=1..19.

Eric Weisstein, Exponential Sum Function.

Formula

a(n) = numerator(Sum_{k=0..n} n^k/k!).

a(n) = A063170(n)/A214402(n) = (n!/A214402(n))*Sum_{k=0..n} n^k/k! for n > 0. - Jonathan Sondow, Jul 16 2012

Example

The first few fractions are 2, 5, 13, 103/3, 1097/12, 1223/5, 47273/72, 556403/315, 10661993/2240, ... = A120266/A214401. - Petros Hadjicostas, May 12 2020

Mathematica

Numerator[Table[Sum[n^k/k!, {k, 0, n}], {n, 1, 30}]]

Crossrefs

Denominators are A214401. Cf. also A063170, A090878, A119029, A120267, A214402.

Sequence in context: A082101 A158712 A090472 * A230518 A241248 A275698

Adjacent sequences: A120263 A120264 A120265 * A120267 A120268 A120269

Keyword

frac,nonn

Author

Alexander Adamchuk, Jun 30 2006

Status

approved