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Production of J/ψ mesons in heavy ion collisions is considered within the statistical coalescence model. The model is in agreement with the experimental data of the NA50 Collaboration for Pb+Pb collisions at 158 AGeV in a wide centrality range, including the so-called “anomalous” suppression domain. The model description of the J/ψ data requires, however, strong enhancement of the open charm production in central Pb+Pb collisions. This model prediction may be checked in the future SPS runs.