In this problem, we will be looking at strings that consist of brackets, '(' and ')'. You are asked to compute how many strings of brackets there are such that the brackets are properly nested. For example, there are two properly nested strings of brackets that are of length 4: "()()" and "(())". Strings "))((", "()((" and ")())" are not properly nested.
The following are all possible properly nested strings of length 6:
1. ()()() 2. (()()) 3. ((())) 4. (())() 5. ()(())
4 5 6 10 60 0
2 0 5 42 3814986502092304