  Pair instability (PI) and pulsational PI prevent the formation of black holes
(BHs) with mass $\gtrsim{}60$ M$_\odot$ from single star evolution. Here, we
investigate the possibility that BHs with mass in the PI gap form via stellar
mergers and multiple stellar mergers, facilitated by dynamical encounters in
young star clusters. We analyze $10^4$ simulations, run with the direct N-body
code nbody6++gpu coupled with the population synthesis code MOBSE. We find that
up to $\sim{}6$~% of all simulated BHs have mass in the PI gap, depending on
progenitor's metallicity. This formation channel is strongly suppressed in
metal-rich (Z = 0.02) star clusters, because of stellar winds. BHs with mass in
the PI gap are initially single BHs but can efficiently acquire companions
through dynamical exchanges. We find that $\sim{}$21%, 10% and 0.5% of all
binary BHs have at least one component in the PI mass gap at metallicity Z =
0.0002, 0.002 and 0.02, respectively. Based on the evolution of the cosmic star
formation rate and metallicity, and under the assumption that all stars form in
young star clusters, we predict that $\sim{}5$~% of all binary BH mergers
detectable by advanced LIGO and Virgo at their design sensitivity have at least
one component in the PI mass gap.
