This is a triplet Afro feel by Art Blakey, one of the major people playing that feel in a hard bop setting in the late 50s/early 60s. I usually call it a 6/8 feel— some people call it 12/8— here the tune is clearly in 4, so we'll call it 12/8. This groove appears to be something he made up, rather than a “correct” African/Latin feel. The bell pattern is derived from our usual pattern, the so-called “short” bell pattern— with the triplets filled out in the last two beats.
On the solos, Blakey goes into a heavy shuffle— the way only he can play it— and stays with it for the rest of the tune, up to the fade out, when he switches back to this feel.
The bass drum is barely audible on the recording, so he could be playing something different for all I know; this matches what the bass player is doing, anyway. The floor tom hit on 4 is softer than the other left hand notes, hence the parentheses.
Listening to the complete track, can you imagine a jazz drummer in a small group today playing as loud as Blakey does, for as long as he does, on this track? He's playing loud. Modern players have basically retired that effect from their playing— that simple, sustained, deep, powerful, groove.