Question about the number of matching brackets in Huawei OJ Training

The questions are as follows:

Parentheses matching

Input n parentheses and output n parentheses that can be combined. For example --

Only () is input;

When the input is 2, there are two types: () and;

When 3 is input, there are (), () and ((())), five types.

There are 14 input values .. And so on.

I think of stupid methods, and so on, because I believe there must be a formula. After a while. I did not summarize it, so I read the book because I have read similar questions in my impressions.

Then the formula is found. Haha.

import java.util.Scanner;  public class Main {        public static void main(String[] args) {            Scanner scanner = new Scanner(System.in);          int n = scanner.nextInt();          scanner.close();          if (n == 0) {        System.out.println(0);}else{  System.out.println((int) (jiecheng(2 * n) / (jiecheng(n) * jiecheng(n) * (n + 1))));  }          }        private static long jiecheng(int n) {          long result = 1;          for (int i = 1; i <= n; i++) {              result *= i;          }          return result;      }  }