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The much used New Orleans piano lick that is basically an extended turn is called the "Famous Lick" by Dr. John and is a staple of any NO playing. It also works its way into other instruments although it lends itself best to piano. I can't find a midi or score of it at first search but will post something later if I find it.

In one of my improv classes (jazz, not comedy) we got a multi page handout of common licks that "every" jazz musician should know, but the short licks did not have names and the longer ones were basically the motif from jazz standards.