We compare [ \alpha /Fe ] , metallicity , and age distributions of globular clusters in elliptical , lenticular , and spiral galaxies , which we derive from Lick line index measurements .
We find a large number of globular clusters in elliptical galaxies that reach significantly higher [ \alpha /Fe ] values ( [ \alpha /Fe ] > 0.5 ) than any clusters in lenticular and spiral galaxies .
Most of these extremely \alpha -enriched globular clusters are old ( t > 8 Gyr ) and cover the metallicity range -1 \lesssim [ Z/H ] \lesssim 0 .
A comparison with supernova yield models suggests that the progenitor gas clouds of these globular clusters must have been predominantly enriched by massive stars ( \gtrsim 20 M _ { \odot } ) with little contribution from lower-mass stars .
The measured [ \alpha /Fe ] ratios are also consistent with yields of very massive pair-instability supernovae ( \sim 130 - 190 M _ { \odot } ) .
Both scenarios imply that the chemical enrichment of the progenitor gas was completed on extremely short timescales of the order of a few Myr .
Given the lower [ \alpha /Fe ] average ratios of the diffuse stellar population in early-type galaxies , our results suggest that these extremely \alpha -enhanced globular clusters could be members of the very first generation of star clusters formed , and that their formation epochs would predate the formation of the majority of stars in giant early-type galaxies .