

A214401


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


5



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
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OFFSET

1,4


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 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.


FORMULA

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


MATHEMATICA

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


PROG

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


CROSSREFS

Numerators are A120266.
Cf. also A063170, A090878, A093101, A119029, A120267, A214402.
Sequence in context: A227106 A085296 A306364 * A009781 A266913 A307027
Adjacent sequences: A214398 A214399 A214400 * A214402 A214403 A214404


KEYWORD

frac,nonn


AUTHOR

Jonathan Sondow, Jul 15 2012


STATUS

approved



