Is there a closed formula for the following sum involving binomials: $\sum_{s=t}^{t+d}\binom{s}{t}\frac{1}{s+1}$ where t,d>=0?
gr8 many thanks, tom. but i'm looking for a formula that does not involve sums or (unresolved) hypergeometric series moreover, the wolfram solution contains the value of the Gamma function for negative integers