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Counting & ProbabilityHardRecursion, Catalan Numbers & Generating Functions

Recursion, Catalan Numbers & Generating Functions · Hard problem

How many solutions in integers (a,b,c,d)(a,b,c,d) are there to a+b+c+d=12a+b+c+d=12 with 0≤a,b,c,d≤50\le a,b,c,d\le 5?