May I share a personal reminiscence regarding this song. My brother was a teenager in the late 1950's (when I was just a toddler) and he had this record in his collection. It soon became a favourite of mine too, and (as all kids do) I had tried to song it myself :)

Later that day my mother mentioned to my brother that I had been trying to sing "some stupid song about a billy-goat: billy-goat this and billy-goat that." My brother, recognising from that fragmentary description what song it was, rushed to my defence and surprised my mother by putting the record on to show her what it actually was that I had been trying to sing.