In the coupon collector problem, I open a cereal box every morning and get a random coupon from a set of $n$ different coupons randomly.
It is known that on average, it will take me $n H_n$ days to get all coupons (at least once).
My question is whether it is known how long it will take me to get $n$ coupons conditional on exactly $k$ coupons being drawn more than one time?