  In this paper we describe explicit generating functions for a large class of
Hurwitz-Hodge integrals. These are integrals of tautological classes on moduli
spaces of admissible covers, a (stackily) smooth compactification of the
Hurwitz schemes.
  Admissible covers and their tautological classes are interesting mathematical
objects on their own, but recently they have proved to be a useful tool for the
study of the tautological ring of the moduli space of curves, and the orbifold
Gromov-Witten theory of DM stacks.
  Our main tool is Atiyah-Bott localization: its underlying philosophy is to
translate an interesting geometric problem into a purely combinatorial one.
