Count me in as another one who had the song stay with him lo these many (33 or so) years. Learned it in elementary school in Pittsburgh, PA in the late 60's. I came to this thread because I now have two boys to whom I want to sing it, and wanted to find the actual melody (the years have messed it up in my head). The melodies provided above didn't have the rhythm so I kept looking (and because I didn't want to go trying to find a Silver Burdett book. )The following URL has it, though as I remember it the beginning two eighth notes are O and Sen-, not Se- and nor, and no "he" before "was a cat." Otherwise it seems to be the way I had learned it.

http://sniff.numachi.com/~rickheit/dtrad/pages/ttDONGATO.html

It would be interesting to know whether this melody is the one most people in this Don Gato Fan Club had learned.