- 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
- <i>Index</i>

# The Central Binomial Coefficient Revisited

# The Central Binomial Coefficient Revisited

- Chapter:
- (p.51) 3 The Central Binomial Coefficient Revisited
- Source:
- Catalan Numbers with Applications
- Author(s):
### Thomas Koshy

- Publisher:
- Oxford University Press

This chapter continues to investigate the central binomial coefficient in much greater detail. Topics explained include Wallis' product, Lucas numbers, Fermat's little theorem, Carlitz's formula, Stirling's asymptotic formula, Fibonacci numbers, Lucas' formula, and Norton's formula.

*Keywords:*
Wallis' product, Stirling's asymptotic formula, binomial probability, Fibonacci numbers, Lucas numbers, Lucas' formula, Fermat's little theorem, Norton's formula, Carlitz's formula

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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
- <i>Index</i>