Bootstrap count vectors ($N_1+\cdots +N_n=n$)

An unordered nonparametric bootstrap sample from $n$ distinct observations is specified by its $n$ nonnegative multiplicities. Stars and bars gives $\left(\genfrac{}{}{0ex}{}{2n-1}{n}\right)$ such vectors. They are not equiprobable: a vector has probability $n!/(n^n{\prod }_i{N}_i!)$, because this counts its ordered sequences of sampled indices.