By just looking up on google:

http://mathematica.stackexchange.com/questions/11632/how-to-generate-a-random-tree

Anyway, if you do go on with your code, would you feel like sharing it? We 
could merge into SymPy a random expression generator, it can always be 
useful.

Easiest way, recursive function picking a random element each time. If it's 
an atom, stop, otherwise call the function recursively on the children 
elements.

You could easily store your node elements in a dictionary, telling you how 
many children there are.

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