http://blog.csdn.net/sunshine_yg/article/details/47685737
卡特兰数 




#include<iostream>  
#include<cstring>  
#include<string>  
#include<cstdio>  
#include<algorithm>  
using namespace std;  
const int base = 10000;  
const int N = 100 + 2;  
int katelan[N][N];  
int main()  
{  
    katelan[1][1] = 1;  
    katelan[2][1] = 2;  
    katelan[3][1] = 5;  
    for (int i = 4; i <= 100; i++)  
    {  
        for (int j =1; j<100; j++)//大数乘法  
        {  
            katelan[i][j] += katelan[i - 1][j] * (4 * i - 2);  
            katelan[i][j + 1] += katelan[i][j] / base;  
            katelan[i][j] %= base;  
        }  
        int temp;  
        for (int j = 100; j > 0; j--)//大数除法  
        {  
            temp=katelan[i][j] % (i + 1);  
            katelan[i][j-1]+=temp* base;  
            katelan[i][j] /= (i + 1);  
        }  
    }  
    int n;  
    while (cin >> n)  
    {  
        int i = 100;  
        while (katelan[n][i] == 0)i--;  
        cout << katelan[n][i--];  
        while (i > 0)  
            printf("%04d", katelan[n][i--]);  
        cout << endl;  
    }  
    return 0;  
}