  Most of the binary black hole (BBH) mergers detected by LIGO and Virgo could
be explained by first-generation mergers formed from the collapse of stars,
while others might come from second (or higher) generation mergers, namely
hierarchical mergers, with at least one of the black holes (BHs) being the
remnant of a previous merger. A primary condition for the occurrence of
hierarchical mergers is that the remnant BHs can be retained by the host star
cluster. We present a simple formula to estimate the hierarchical merger rate
in star clusters. We find this latter to be proportional to the retention
probability. Further, we show that $\sim 2\%$ of BBH mergers in nuclear star
clusters (NSCs) may instead be of hierarchical mergers, while the percentage in
globular clusters (GCs) is only a few tenths of a percent. However, the rates
of hierarchical merger in GCs and NSCs are about the same, namely of $\sim
{\mathcal O(10^{-2})}~{\rm Gpc^{-3}~yr^{-1}}$, because the total BBH merger
rate in GCs is larger than that in NSCs. This suggests that if a
gravitational-wave event detected by LIGO-Virgo is identified as a hierarchical
merger, then it is equally likely that this merger originated from a GC or an
NSC.
