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We present an analysis of inclusive Omega_c^0 baryon production and
decays in 230.5 fb^-1 of data recorded with the BABAR detector at the
PEP-II asymmetric-energy e+ e- collider at the Stanford Linear
Accelerator Center. Omega_c^0 baryons are reconstructed in four final
states (Omega- pi+, Omega- pi+ pi0, Omega- pi+ pi+ pi-, Xi- K- pi+ pi+)
and the ratios of branching fractions for these final states are
measured. We also measure the momentum spectrum of the Omega_c^0 baryons
in the e+ e- center-of-mass frame. From the spectrum, we observe
Omega_c^0 production from B decays and in ccbar events, and extract the
two rates of production.