 The first seven Catalan numbers are \(C_0=1\), \(C_1=1\), \(C_2=2\),  \(C_3=5\), \(C_4=14\), \(C_5=42\) and \(C_6=132\).  As an illustration, we may take—for simplicity—strings consisting of \(x\)s, because the terms are to differ only in their grouping. Clearly, if the term is \(x\) or \(xx\), that is of length 1 or 2, then there is only one way to form a term, that is, there exists just one possible term in each case. If we start with three \(x\)s, then we may form \((xx)x\) or \(x(xx)\). If the length of the term is 4, then the five terms are: \(xxxx\), \(x(xx)x\), \(xx(xx)\), \(x(xxx)\) and \(x(x(xx ))\). (It is a useful exercise to try to list the 14 distinct terms that can be formed from 5 \(x\)s.)