Note that a product x1x2x3 may be parenthesized in two
Chapter 9, Problem 9.126(choose chapter or problem)
Note that a product x1x2x3 may be parenthesized in two different ways: (x1x2)x3 and x1(x2x3). Similarly, there are several different ways to parenthesize x1x2x3x4. Two such waysare (x1x2)(x3x4) and x1((x2x3)x4).LetPn bethenumberofdifferentwaystoparenthesizetheproduct x1x2 ...x4. Show that if P1 =1, then Pn = n1k=1 Pk Pnk for all integers n 2. (It turns out that the sequence P1, P2, P3,...is the same asthesequenceofCatalannumbers: Pn =Cn1 forallintegers n 1. See Example 5.5.4.)
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