  The lack of observations of abundance patterns originating in
pair-instability supernovae has been a long-standing problem in relation to the
first stars. This class of supernovae is expected to have an abundance pattern
with a strong odd-even effect, making it substantially different from
present-day supernovae. In this study, we use a cosmological radiation
hydrodynamics simulation to model such supernovae and the subsequent formation
of the second generation of stars. We incorporate streaming velocities for the
first time. There are 14 star-forming minihalos in our
$1\,\mathrm{Mpc}\,h^{-1}$ box, leading to 14 supernovae occurring before
redshift $z=19.5$, where we start reducing the complexity of the simulation.
Following the explosions, extremely metal-poor stars form in 10 halos via
internal and external enrichment, which makes it the most common outcome. Only
one halo does not recollapse during the simulations. This result is at tension
with the current (lack of) observations of metal-poor stars with pair
instability supernova abundance patterns, suggesting that these very massive
stars might be rare even in the early Universe. The results from this
simulation also give us insights into what drives different modes of recollapse
and what determines the mixing behavior of metals after very energetic
supernovae.
