luogu 1044

卡特兰数的模板题
卡特兰数公式$h(n) = h(0) * h(n-1)+h(1) * h(n -2)+……+h(n-1)*h(0)$
还有另一种时间更优的递推
$h(n) = h(n - 1)*（4*n-2)/(n+ 1)$

for(int i = 2; i <= n; i ++) {
    ans[i] = ans[i - 1] * (4 * n - 2) / (n + 1);
}

#include <cstdio>

using namespace std;

int n, ans[20];

int read() {
    int f = 1, k = 0;
    char c = getchar();
    while(c < '0' || c > '9') {
        if(c == '-') {
            f = -1;
        }
        c = getchar();
    }
    while(c >= '0' && c <= '9') {
        k = k * 10 + c - '0';
        c = getchar();
    }
    return f * k;
}


int main() {
    n = read();
    ans[0] = 1;
    ans[1] = 1;
    for(int i = 2; i <= n; i ++) {
        for(int j = 0; j < i; j ++) {
            ans[i] += ans[j] * ans[i - j - 1];
        }
    }
    printf("%d", ans[n]);
    return 0;
}