Unique Binary Search Trees

Problem

Given n, how many structurally unique BSTs (binary search trees) that store values 1...n?

Example

Given n = 3, there are a total of 5 unique BST's.

    1           3    3       2      1
     \         /    /       / \      \
      3      2     1       1   3      2
     /      /       \                  \
    2     1          2                  3