Enumerating complex rank $n$ vector bundles on $\mathbb{C}{P}^{n+1}$

We enumerate complex rank $n$ topological vector bundles on $\mathbb{C}{P}^{n+1}$ with prescribed Chern classes. This extends work of Atiyah and Rees in the case $n=2$ and work of Hu in the case that all Chern classes are zero.