Find the number of valid parentheses expressions of given length | 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 ) ; Function to find possible ways to put balanced parenthesis in an expression of length n ; If n is odd , not possible to create any valid parentheses ; Otherwise return n / 2 'th  Catalan Number ; Driver Code
function binomialCoeff ( n , k ) { let res = 1 ; if ( k > n - k ) k = n - k ; for ( let i = 0 ; i < k ; ++ i ) { res *= ( n - i ) ; res /= ( i + 1 ) ; } return res ; } function catalan ( n ) { let c = binomialCoeff ( 2 * n , n ) ; return c / ( n + 1 ) ; } function findWays ( n ) { if ( n & 1 ) return 0 ; return catalan ( n / 2 ) ; } let n = 6 ; document . write ( " " + n + " " + findWays ( 6 ) ) ;