

A119029


Numerator of Sum_{k=1..n} n^(k1)/k!.


6



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

1,2


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.


FORMULA

a(n) = numerator(Sum_{k=1..n} n^(k1)/k!).
a(n) = A120267(n)/n.


EXAMPLE

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


MATHEMATICA

Numerator[Table[Sum[n^(k1)/k!, {k, 1, n}], {n, 1, 30}]]


CROSSREFS

Cf. A063170, A090878, A093101, A120266, A120267, A214401 (denominators), A214402.
Sequence in context: A103099 A342665 A266495 * A291144 A162120 A162121
Adjacent sequences: A119026 A119027 A119028 * A119030 A119031 A119032


KEYWORD

frac,nonn


AUTHOR

Alexander Adamchuk, Jul 22 2006


STATUS

approved



