Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations

A classical scheme of random equiprobable allocations of $n$ particles into $N$ cells is considered. We find an asymptotic formula for the probability that the number of empty cells is equal to $k$ under the condition that $n, N \to \infty$ in such a way that $n/(N - k)$ is bounded and separated from 1 from below.