Recent examination of large samples of ω Cen giants shows that, as in mono-metallic globular clusters, sodium versus oxygen anticorrelation is present 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 ω Cen is more complex than that of mono-metallic clusters, it shares some key steps with those simpler clusters. 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 (AGB) stars in the same range of metallicity, suggesting that the stars at [Fe/H] > -1.3 in ω 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 protocluster 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 relatively metal-rich 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 ω Cen took place in a few 108 yr, and discuss the problem of a prompt formation of s-process elements.