  In this paper, we study the secular dynamical evolution of binaries composed
of intermediate-mass and stellar-mass black holes (IMBHs and SBHs,
respectively) in orbit about a central super-massive black hole (SMBH) in
galactic nuclei. Such BH triplets could form via the inspiral of globular
clusters toward galactic nuclei due to dynamical friction, or even major/minor
galaxy mergers. We perform, for reasonable initial conditions that we justify,
sophisticated $N$-body simulations that include both regularization and
Post-Newtonian corrections. We find that mass segregation combined with
Kozai-Lidov oscillations induced by the primary SMBH can effectively merge
IMBH-SBH binaries on time-scales much shorter than gravitational wave emission
alone. Moreover, the rate of such extreme mass ratio inspirals could be high
($\sim 1\ \mathrm{Gpc}^{-3}\ \mathrm{yr}^{-1}$) in the local Universe, but
these are expected to be associated with recent GC infall or major/minor
mergers, making the observational signatures of such events (e.g., tidal
debris) good diagnostics for searching for SMBH-IMBH-SBH mergers. A small
fraction could also be associated with tidal disruption events by the IMBH-SBH
during inspiral.
