  Gravitational waves (GWs) offer an unprecedented opportunity to survey the
sky and detect mergers of compact objects. While intermediate-mass black holes
(IMBHs) have not been detected beyond any reasonable doubt with either
dynamical or accretion signatures, the GW landscape appears very promising.
Mergers of an IMBH with a supermassive black hole (SMBH) will be primary
sources for the planned space-based mission LISA and could be observed up to
the distant Universe. SMBH-IMBH binaries can be formed as a result of the
migration and merger of stellar clusters at the center of galaxies, where an
SMBH lurks. We build for the first time a semi-analytical framework to model
this scenario, and find that the the comoving merger rate of SMBH-IMBH binaries
is $\sim 10^{-4}$ Gpc$^{-3}$ yr$^{-1}$ in the local Universe for a unity IMBH
occupation fraction, scales linearly with it, and has a peak at $z\approx
0.5$-$2$. Our model predicts $\sim 0.1$ event yr$^{-1}$ within redshift
$z\approx 3.5$ if $10\%$ of the inspiralled star clusters hosted an IMBH, while
$\sim 1$ events yr$^{-1}$ for a unity occupation fraction. More than $90\%$ of
these systems will be detectable with LISA with a signal-to-noise ratio larger
than $10$, promising to potentially find a family of IMBHs.
