We consider the alternating sums
![$ S^{(m)}_n = \sum_{k=0}^n (-1)^{n-k}
k^m {n \choose k}^{-1}$](img2.gif)
, recently studied by Belbachir, Rahmani, and
Sury, and obtain some results complementary to those found by the three
authors, especially for what concerns generating functions, closed
forms and asymptotic approximation.