  We propose a scenario in which massive stars form at the outer edges of an
AGN accretion disc. We analyze the dynamics of a disc forming around a
supermassive black hole, in which the angular momentum is transported by
turbulence induced by the disc's self-gravity. We find that once the surface
density of the disc exceeds a critical value, the disc fragments into dense
clumps. The biggest clumps collapse and form massive stars, which produce
few-tens-solar-mass black holes at the end of their evolution. The embedded
black holes will interact gravitationally with the massive accretion disc and
be dragged towards the central black hole. Merger of a disc-born black hole
with the central black hole will produce a burst of gravitational waves. If the
central black hole is accreting at a rate comparable to the Eddington limit,
the gas drag from the accretion disc will not alter significantly the dynamics
of the final year of merger, and the gravitational waves should be observable
by LISA. We argue that for a reasonable range of parameters such mergers will
be detected monthly, and that the gravitational-wave signal from these mergers
is distinct from that of other merger scenarios. Also, for some plausible black
hole masses and accretion rates, the burst of gravitational waves should be
accompanied by a detectable change in the optical luminosity of the central
engine.
