  Repeated mergers of stellar-mass black holes (BHs) in dense star clusters can
produce intermediate-mass black holes (IMBHs). In particular, nuclear star
clusters at the centers of galaxies have deep enough potential wells to retain
most of the BH merger products, in spite of the significant recoil kicks due to
anisotropic emission of gravitational radiation. These events can be detected
in gravitational waves (GWs), which represent an unprecedented opportunity to
reveal IMBHs. In this paper, we analyze the statistical results of a wide range
of numerical simulations, which encompass different cluster metallicities,
initial BH seed masses, and initial BH spins, and we compute the merger rate of
IMBH binaries. We find that merger rates are in the range
$0.01$-$10$\,Gpc$^{-3}$\,yr$^{-1}$ depending on IMBH masses. We also compute
the number of multi-band detections in ground-based and space-based
observatories. Our model predicts that a few merger events per year should be
detectable with LISA, DECIGO, ET, and LIGO for IMBHs with masses $\lesssim
1000\msun$, and a few tens of merger events per year with DECIGO, ET, and LIGO
only.
