A120267 Numerator of Sum_{k=1..n} n^k/k!.

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

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^(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.

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