  The advanced LIGO O3a run catalog has been recently published, and it
includes several events with unexpected mass properties, including mergers with
individual masses in the lower and upper mass gaps, as well as mergers with
unusually small mass ratios between the binary components. Here we entertain
the possibility that these outliers are the outcome of hierarchical mergers of
black holes or neutron stars in the dense environments of globular clusters. We
use the coagulation equation to study the evolution of the black hole mass
function within a typical cluster. Our prescription allows us to monitor how
various global quantities change with time, such as the total mass and number
of compact objects in the cluster, its overall merger rate, and the probability
to form intermediate-mass black holes via a runaway process. By accounting for
the LIGO observational bias, we predict the merger event distributions with
respect to various variables such as the individual masses M1 and M2, their
ratio q, and redshift z, and we compare our predictions with the published O3a
data. We study how these distributions depend on the merger-rate and ejections
parameters and produce forecasts for the (tight) constraints that can be placed
on our model parameters using the future dataset of the O5 run. Finally, we
also consider the presence of a static channel with no coagulation producing
merger events alongside the dynamic channel, finding that the two can be
distinguished based solely on the merger mass distribution with future O5 data.
