A214401 Denominator of Sum_{k=0..n} n^k/k!.

1, 1, 1, 3, 12, 5, 72, 315, 2240, 567, 1814400, 77, 239500800, 868725, 7175168, 49116375, 2092278988800, 14889875, 3201186852864000, 14849255421, 3783802880000, 3543572316375, 562000363888803840000, 2505147019375, 496358721386591551488

Offset: 1

Author

Jonathan Sondow, Jul 15 2012

Keywords

• frac
• nonn

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 the current sequence. This, however, is not immediately obvious. - Petros Hadjicostas, May 12 2020

Links

• Michel Marcus, Table of n, a(n) for n = 1..150
• Eric Weisstein, Exponential Sum Function.

Crossrefs

Numerators are A120266.

Cf. also A063170, A090878, A093101, A119029, A120267, A214402.

Programs

Mathematica

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

PARI

a(n) = denominator(sum(k=0, n, n^k/k!)); \\ Michel Marcus, Apr 20 2021

Formula

a(n) = n!/A214402(n).