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Show that the Catalan numbers count the following. (a) Sequences (1, 2,..., æn) of positive integers such that 1 ≤ 2 ≤ ...an and for each i, a ≤i. For example, for n = 3, the sequences counted are 111, 112, 113, 122, 123.

Show that the Catalan numbers count the following. (a) Sequences (1, 2,..., æn) of positive integers such that 1 ≤ 2 ≤ ...an and for each i, a ≤i. For example, for n = 3, the sequences counted are 111, 112, 113, 122, 123.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Show that the Catalan numbers count the following. (a) Sequences (1, 2,..., n) of positive integers such that #₁ ≤ x2 ≤ ..<n and for each i, x, ≤i. = 3, the sequences counted are 111, 112, 113, 122, 123. For example, for n
Transcribed Image Text:1. Show that the Catalan numbers count the following. (a) Sequences (1, 2,..., n) of positive integers such that #₁ ≤ x2 ≤ ..<n and for each i, x, ≤i. = 3, the sequences counted are 111, 112, 113, 122, 123. For example, for n
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