 Title Pages
 Dedication
 Preface
 Symbols

1 Binomial Coefficients 
2 The Central Binomial Coefficient 
3 The Central Binomial Coefficient Revisited 
4 Binomial Coefficients Revisited 
5 Catalan Numbers 
6 The Ubiquity of Catalan Numbers I 
7 The Ubiquity of Catalan Numbers II 
8 Tress and Catalan Numbers 
9 Lattice Paths and Catalan Numbers 
10 Partitions and Catalan Numbers 
11 Algebra, Sports, and Catalan Numbers 
12 Pascal' Triangle and Catalan Numbers 
13 Divisibility Properties 
14 A Catalan Triangle 
15 A Family of Binary Words 
16 Tribinomial Coefficients 
17 Generalized Catalan Numbers  Appendix A

Appendix B The First 100 Catalan Numbers  References
 Index of Mathematicians
 Index
Catalan Numbers
Catalan Numbers
 Chapter:
 (p.103) 5 Catalan Numbers
 Source:
 Catalan Numbers with Applications
 Author(s):
Thomas Koshy
 Publisher:
 Oxford University Press
This chapter presents Catalan numbers in an interesting, historical perspective, beginning with the wellknown triangulation problem. In addition, it develops three recursive formulas for C_{n}, an approximate value for C_{n}, a relationship with the gamma function, and Shapiro's identity. It also shows how the parenthesization and triangulation problems are closely related.
Keywords: triangulation problem, gamma function, reflection formula, Shapiro's identity, superfactorials
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 Title Pages
 Dedication
 Preface
 Symbols

1 Binomial Coefficients 
2 The Central Binomial Coefficient 
3 The Central Binomial Coefficient Revisited 
4 Binomial Coefficients Revisited 
5 Catalan Numbers 
6 The Ubiquity of Catalan Numbers I 
7 The Ubiquity of Catalan Numbers II 
8 Tress and Catalan Numbers 
9 Lattice Paths and Catalan Numbers 
10 Partitions and Catalan Numbers 
11 Algebra, Sports, and Catalan Numbers 
12 Pascal' Triangle and Catalan Numbers 
13 Divisibility Properties 
14 A Catalan Triangle 
15 A Family of Binary Words 
16 Tribinomial Coefficients 
17 Generalized Catalan Numbers  Appendix A

Appendix B The First 100 Catalan Numbers  References
 Index of Mathematicians
 Index