Unique Binary Search Trees

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

For 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

Solution:
1-d dynamic programming.

public class Solution {
    public static int numTrees(int n) { 
        int[] sum = new int[n+1];
        sum[0] = 1;
        sum[1] = 1;
        for(int i = 2; i <= n; i++){
            sum[i] = 0;
            for(int j=1; j<=i; j++){
                int leftSum = j-1;
                int rightSum = i-j;
                sum[i] += (sum[leftSum] * sum[rightSum]);
            }
        }
        return sum[n];
    }
}