LeetCode_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

Analysis: Just recursively count the number of left sub tree times number of right sub tree.

class Solution {
public:
    int calculate(int n){
        int sum = ;
        for(int i = ; i< n ;i++ )
            sum += tree[i] * tree[n--i] ;
        // tree[i] : left subTree  tree[n-1-i] " right subTree
        return sum ;
    }
    int numTrees(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
         tree.resize(n+,);
         for(int i = ; i <= n ; i++)
              tree[i] = calculate(i);
        return tree[n] ;

    }
private :
  vector<int> tree;
};