Number of strings of length 2*n of up to n different types t(k) of balanced parentheses, where the first appearance of type t(k) must precede the appearance of t(k+1) for all k<n.
For example, from the 5 parenthesis string of length 3
1: ()()(); 2: ()(()); 3: (())(); 4: (()()); 5: ((())).
we obtain the B(3) * C(3) = 5 * 5 = 25 strings
1: ()()(), ()()[], ()[](), ()[][], ()[]{};
2: ()(()), ()([]), ()[()], ()[[]], ()[{}];
3: (())(), (())[], ([])(), ([])[], ([]){};
4: (()()), (()[]), ([]()), ([][]), ([]{});
5: ((())), (([])), ([()]), ([[]]), ([{}]).
(End)
