Recall that the number of unique binary trees with n nodes is given by the nth Catalan number, which can be computed using the formula: C(n) = (2n)! / ((n+1)! * n!).

Consider how the Catalan numbers can be derived using dynamic programming by breaking down the problem into smaller subproblems (e.g., the number of trees with root and left/right subtrees).

Explore the recursive relationship of Catalan numbers: C(n) = sum(C(i) * C(n-i-1)) for i from 0 to n-1, and use memoization or tabulation to optimize the computation.