Number of Permutations such that no Three Terms forms Increasing Subsequence | Java program to find the nth catalan number ; Returns value of Binomial Coefficient C ( n , k ) ; Since C ( n , k ) = C ( n , n - k ) ; Calculate value of [ n * ( n - 1 ) * -- - * ( n - k + 1 ) ] / [ k * ( k - 1 ) * -- - * 1 ] ; A Binomial coefficient based function to find nth catalan number in O ( n ) time ; Calculate value of 2 nCn ; return 2 nCn / ( n + 1 ) ; Driver code
import java . io . * ; class GFG { static long binomialCoeff ( long n , long k ) { long res = 1 ; if ( k > n - k ) k = n - k ; for ( int i = 0 ; i < k ; ++ i ) { res *= ( n - i ) ; res /= ( i + 1 ) ; } return res ; } static long catalan ( long n ) { long c = binomialCoeff ( 2 * n , n ) ; return c / ( n + 1 ) ; } public static void main ( String [ ] args ) { int n = 3 ; System . out . println ( catalan ( n ) ) ; } }