  We provide predictions for charmonium and open charm production in nuclear
collisions at SPS/FAIR energies within the framework of the statistical
hadronization model. The increasing importance at lower energies of Lambda_c
production is demonstrated and provides a challenge for future experiments. We
also demonstrate that, because of the large charm quark mass and the different
timescales for charm quark and charmed hadron production, possible
modifications of charmed hadrons in the hot hadronic medium do not lead to
measurable changes in cross sections for D-meson production. A possible
influence of medium effects can be seen, however, in yields of charmonium.
These effects are visible at all energies and results are presented for the
energy range between charm threshold and RHIC energy.
