Preface. List of Symbols. Leonardo Fibonacci. The Rabbit Problem. Fibonacci Numbers in Nature. Fibonacci Numbers: Additional Occurrances. Fibonacci and Lucas Identities. Geometric Paradoxes.… Expand

1. Bionomial Coefficients 2. The Central Binomial Coefficient 3. The Central Binomial Coefficient Revisited 4. Binomial Coeffiecients Revisited 5. Catalan Numbers 6. The Ubiquity of Catalan Numbers I… Expand

Fundamentals Divisibility Theory Canonical Decompositions Linear Diophantine Equations and Congruences Congruences Applications Systems of Linear Congruences Three Classical Milestones Multiplicative… Expand

Catalan numbers, like Fibonacci and Lucas numbers, appear in a variety of situ ations, including the enumeration of triangulations of convex polygons, well-formed sequences of parentheses, binary… Expand

Summary This article studies the convergence of the infinite series of the reciprocals of the Catalan numbers. We extract the sum of the series as well as some related ones, illustrating the power of… Expand