I tried to figure out following problem, but failed :/ My best guess is that it somehow is a mixture of a binomial and a hypergeometric distribution:
I have an urn with N white balls and 0 black balls. Every time I draw one white ball, I replace it with a black ball. A drawn black ball stays black (and is put back in the urn). I'm particularly interested in the mean of white balls in the urn after n draws.