We are collecing stickers in chocolate bars and whenever we open a bar we get a random new sticker. There are many different stickers and we try to collect them all.
We open the first bar and get a sticker. We open the second bar and we get another sticker, but there is now a chance that it's the one we already got. Doubles are thrown away. As we collect more and more different stickers, the chance gets worse and worse.
So if there are a total of $N$ different possible stickers and we already got $n$, how much chocolate bars $d(N,n)$ do we have to open before we get another one, i.e. the $(n+1)^{th}$ sticker? From this it should also be possible to compute the total number of bars we have to open (sum of average openings).