

A120267


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


6



1, 4, 12, 100, 1085, 1218, 47201, 556088, 10659753, 7281020, 62927202701, 7217988, 60718623181177, 595952851172, 13324959230295, 247016251998448, 28505095507110827053, 549689328228186, 320305941258100632731917
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OFFSET

1,2


COMMENTS

n divides a(n) and a(n)/n = A119029(n).  Alexander Adamchuk, Oct 08 2006
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^k/k!).
a(n) = n*A119029(n).  Alexander Adamchuk, Oct 08 2006


EXAMPLE

The first few fractions are 1, 4, 12, 100/3, 1085/12, 1218/5, 47201/72, 556088/315, 10659753/2240, 7281020/567, ... = A120267/A214401.  Petros Hadjicostas, May 12 2020


MATHEMATICA

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


CROSSREFS

Cf. A063170, A090878, A093101, A119029, A120266, A214401 (denominators), A214402.
Sequence in context: A268363 A038053 A217155 * A012278 A070040 A079822
Adjacent sequences: A120264 A120265 A120266 * A120268 A120269 A120270


KEYWORD

frac,nonn


AUTHOR

Alexander Adamchuk, Jun 30 2006


EXTENSIONS

Various sections edited by Petros Hadjicostas, May 12 2020~


STATUS

approved



