How many samples does it take to see all the balls in an urn?

Let an urn containN balls, numbered from 1 toN. A random number of balls are drawn without replacements from the urn, their numbers are noted and the balls are then returned to the urn. This is done repeatedly, the sample sizes being independent identically distributed. Letv be the number of samples needed to see all the balls. A simple approximation forEv and the asymptotic distribution ofv asN → ∞ are obtained.