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

class Solution {
public:
int numTrees(int n) {
if(n==1)
return 1;
else
return numTrees(n-1)*(4*n-2)/(n+1);
}
};卡特兰数:
f(n) = f(n-1)*(4n-2)/(n + 1)
f(0) = 1;
f(1) = 1

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670,
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