(组合数学3.1.2.2)POJ 2084 Game of Connections(卡特兰数公示的实现)

package com.njupt.acm;

import java.math.BigInteger;
import java.util.Scanner;

public class POJ_2084 {

	public static void main(String[] args) {
		BigInteger catalan[] = new BigInteger[102];
		catalan[1] = new BigInteger("1");

		BigInteger one = new BigInteger("1");
		BigInteger two = new BigInteger("2");
		BigInteger four = new BigInteger("4");

		int i;
		for(i = 1 ; i <= 100 ; ++i){

			catalan[i+1] = catalan[i].multiply(four.multiply(new BigInteger(i + "")).subtract(two)).divide(new BigInteger(i + "" ).add(one));

		}

		Scanner scanner = new Scanner(System.in);
		int n ;

		while(true){
			n = scanner.nextInt();
			if(n < 0){
				break;
			}

			System.out.println(catalan[n + 1]);
		}

	}
}