ON A QUEER BINOMIAL SUM

In this paper the binomial sum S-n(r) = (m=0) Sigma (n) ((n)(m)) (-1)( m)/m(r)+1 (r > 0, n epsilon N) is investigated. It turns out that the behaviour of this sum for n --> infinity depends on the parameter r an d changes dramatically at the values r = 1 and r = 2. In particular, f or r greater than or equal to 2 we obtain an oscillatory behaviour whi le for r<2 the sequence S-n(r) is monotonous at least for large values of n.