Here's an example of "Down ByThe Banks Of The Hanky Panky" that I hadn't seen or heard before. This example combines the rhyme "Fouble Double This" and the rhyme "Down By The Banks Of The Hanky Panky":


double double this this double double that that double this double that double double this that! single single this this... ect. -down by the bay with the hanky panky where the bull frog frog jumps from bank to bank he says hip hop dilli-op-she-bop, last one outs a bullfrog let me hear ya say 1, 2, 3... - Tue Dec 28 2004

http://www.homeschool.co.uk/resource/jump-rope/jump-rope-rhymes.html
Christian Home Education- Jump Rope Rhymes

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Unfortunately, no information is given on that page as to who chanted this rhyme or where {city, state or province & country}.