  Recent exam of large samples of omega Cen giants shows that it shares with
mono-metallic globular clusters the presence of the sodium versus oxygen
anticorrelation, within each subset of stars with iron content in the range
-1.9<~[Fe/H]<~-1.3. These findings suggest that, while the second generation
formation history in omega Cen is more complex than that of mono-metallic
clusters, it shares some key steps with those simpler cluster. In addition, the
giants in the range -1.3<[Fe/H]<~-0.7 show a direct O--Na correlation, at
moderately low O, but Na up to 20 times solar. These peculiar Na abundances are
not shared by stars in other environments often assumed to undergo a similar
chemical evolution, such as in the field of the Sagittarius dwarf galaxy. These
O and Na abundances match well the yields of the massive asymptotic giant
branch stars (AGB) in the same range of metallicity, suggesting that the stars
at [Fe/H]>-1.3 in omega Cen are likely to have formed directly from the pure
ejecta of massive AGBs of the same metallicities. This is possible if the
massive AGBs of [Fe/H]>-1.3 in the progenitor system evolve when all the
pristine gas surrounding the cluster has been exhausted by the previous star
formation events, or the proto--cluster interaction with the Galaxy caused the
loss of a significant fraction of its mass, or of its dark matter halo, and the
supernova ejecta have been able to clear the gas out of the system. The absence
of dilution in the metal richer populations lends further support to a scenario
of the formation of second generation stars in cooling flows from massive AGB
progenitors. We suggest that the entire formation of omega Cen took place in a
few 10^8yr, and discuss the problem of a prompt formation of s--process
elements.
