  In previous work we have shown that the equivariant index of multi-centered
N=2 black holes localizes on collinear configurations along a fixed axis. Here
we provide a general algorithm for enumerating such collinear configurations
and computing their contribution to the index. We apply this machinery to the
case of black holes described by quiver quantum mechanics, and give a
systematic prescription -- the Coulomb branch formula -- for computing the
cohomology of the moduli space of quiver representations. For quivers without
oriented loops, the Coulomb branch formula is shown to agree with the Higgs
branch formula based on Reineke's result for stack invariants, even when the
dimension vector is not primitive. For quivers with oriented loops, the Coulomb
branch formula parametrizes the Poincar\'e polynomial of the quiver moduli
space in terms of single-centered (or pure-Higgs) BPS invariants, which are
conjecturally independent of the stability condition (i.e. the choice of
Fayet-Iliopoulos parameters) and angular-momentum free. To facilitate further
investigation we provide a Mathematica package "CoulombHiggs.m" implementing
the Coulomb and Higgs branch formulae.
