Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.
"Local limit theorems for finite and infinite urn models." Ann. Probab. 36 (3) 992 - 1022, May 2008. https://doi.org/10.1214/07-AOP350