Poj 2084 Catalan count

[Question ]:

There are 2 * n consecutive numbers on a ring. Calculate the number of methods that concatenate these two numbers and their connected edges do not intersect.

[Knowledge point ]:

Mathematics + Catalan count

H (1) = 1, h (0) = 1

Recursion 1: H (n) = H (0) * H (n-1) + H (1) * H (n-2) +... + H (n-1) H (0) (N> = 2)

Recursion 2: H (n) = (4 * N-2)/(n + 1) * H (n-1 );

The recursive relationship is interpreted as H (n) = C (2n, N)/(n + 1) (n = 1, 2, 3 ,...)

[Question ]:

For typical applications of Catalan, the answer to 2 * n is H (n ).

[Code ]:

 1 import java.io.*; 2 import java.util.*; 3 import java.math.*; 4  5 public class Main { 6     public static void main(String args[]){ 7         Scanner cin = new Scanner( 8         new BufferedInputStream(System.in)); 9         BigInteger[] B = new BigInteger[120];10         B[0] = new BigInteger("1");11         B[1] = new BigInteger("1");12         for(int i = 2; i <= 100; i++){13             B[i] = B[i - 1].multiply(14             BigInteger.valueOf(4 * i - 2)).divide(15             BigInteger.valueOf(i + 1));16         }17         while(true){18             int n = cin.nextInt();19             if(n == -1)20                 break;21             System.out.println(B[n]);22         }23     }24 }