卡特兰数:

$C_{2n}^n-C_{2n}^{n-1} = \dfrac{C_{2n}^n}{n+1}$

package 数学;

import java.util.Scanner;

public class 满足条件的01序列 {
    static int m = 1000000007;
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        long res = 1;
        for(int i = 1,j = 2*n; i <= n;i ++,j--) {
            res = res * j % m;
            res = res * qmi(i,m-2,m)%m;
        }
        System.out.println(res*qmi(n+1,m-2,m)%m);
    }
    private static long qmi(long a, int k, int m) {
        long res = 1;
        while(k!=0) {
            if((k&1)==1) res = res * a %m;
            a = a*a%m;
            k>>=1;
        }
        return res;
    }
}