CSU1576---Catalan Square(卡特蘭數&&大整數)

思路：

關於卡特蘭數：

遞推公式：C(n)=C(n-1)*((4*n-2)/(n+1));

import java.math.BigInteger;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		String s, L;
		BigInteger Catalan[] = new BigInteger[5001];
		Catalan[0] = Catalan[1] = BigInteger.valueOf(1);
		BigInteger one = BigInteger.valueOf(1);
		BigInteger two = BigInteger.valueOf(2);
		BigInteger four = BigInteger.valueOf(4);
		Scanner cin = new Scanner(System.in);
		int n = cin.nextInt();
		for (int i = 2; i <= n; i++) {
			Catalan[i] = Catalan[i - 1].multiply(((BigInteger.valueOf(i).multiply(four)).subtract(two)))
					.divide(BigInteger.valueOf(i).add(one));
		}
		BigInteger ans = BigInteger.valueOf(0);
		for (int i = 0; i <= n; i++) {
			ans = ans.add(Catalan[i].multiply(Catalan[n - i]));
		}
		System.out.print(ans);
	}
}