

A120266


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


9



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

1,1


COMMENTS

Apparently, the three sequences T_1(n) = Sum_{k=1..n} n^(k1)/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



