OFFSET
1,2
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 A214401. This, however, is not immediately obvious. - Petros Hadjicostas, May 12 2020
FORMULA
a(n) = numerator(Sum_{k=1..n} n^(k-1)/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^(k-1)/k!, {k, 1, n}], {n, 1, 30}]]
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jul 22 2006
STATUS
approved