The origins of this song go back way before the recording era to around the same time as the origin of the Mardi Gras Indians. The song most like the one we know today was originally recorded by Sugar Boy Crawford as "Jock-a-mo" in 1953. The first version to enter popular consciousness was by The Dixie Cups around 1965 (revived by the movie "Rain Man"). My own personal favourite is Dr John's from around 1972.