Marvin Hamlisch composed the scores to Woody Allen's first two films.
Here is the theme from BANANAS performed by singers Rena Strober and Stephen Van Dorn, and pianist Mike Farrell. Adam Shell and Nicholas Kraft add some rhythm.
This whole thing is being sight-read for the first time to capture the fun of improv.
BANANAS
Here is a link to a checklist of Sheet Music from which this was chosen.