Merge pull request #1 from xingjiapeng/xingjiapeng-patch-1

H_n = \binom{2n}{n} - \binom{2n}{n-1}

$$

```

f[n] = f[0] * f[n - 1] + f[1] * f[n - 2] + ... + f[n - 1] * f[0]

```

具体实例

[https://www.luogu.org/problem/P1044](洛谷 P1044 栈)

```

#include <iostream>

using namespace std;

int n;

long long f[25];

int main(){

	f[0] = 1;

	cin >> n;

	for(int i = 1; i <= n; i++)

		f[i] = f[i - 1] * (4 * i - 2) / (i + 1);

    //这里用的是常见公式2

	cout << f[n] << endl;

	return 0;

}

```

## 路径计数问题

非降路径是指只能向上或向右走的路径。