Leetcode: Unique Binary Search Trees in C++

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:
int numTrees(int n) {
        vector<int> count(n+1, 0);
        count[0] = 1;
        count[1] = 1;
        for(int i=2;i<=n;i++)
        {
            for(int j=0;j<i;j++)
            count[i] += count[j]*count[i-j-1];
        }
        return count[n];
    }