A binary bracketing is a bracketing built up entirely of binary operations. The number of binary bracketings of n letters (Catalan's problem) are given by the Catalan numbers C_(n - 1), where C_n | congruent | 1/(n + 1)(2n n) | = | 1/(n + 1) ((2n)!)/(n!^2) = ((2n)!)/((n + 1)!n!),

bracketing | Catalan number | Catalan's problem