In an attempt to fix mis-matched parenthesis you attempt all the possible configuration, but you quickly realize how messy it is.

How many distinct valid parentheses permutations are possible for 50 expressions?

Details and Assumptions

As an explicit example the number of valid permutations of 4 parentheses is 2: (( )) and ()().

All the opening parentheses have a matching closing parentheses.

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