A short proof of an identity of Touchard's concerning Catalan numbers

DOI10.1016/0097-3165(76)90034-0zbMath0337.05012OpenAlexW2080638745MaRDI QIDQ1229870

Louis W. Shapiro

Publication date: 1976

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(76)90034-0

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (18)

Protected Branches in Ordered Trees ⋮ Positive Definite Matrices and Catalan Numbers, Revisited ⋮ Ears of triangulations and Catalan numbers ⋮ Differential equations associated with Catalan-Daehee numbers and their applications ⋮ Reductions of binary trees and lattice paths induced by the register function ⋮ The Riordan group ⋮ On the structure of the lattice of noncrossing partitions ⋮ Deux propriétés combinatoires des nombres de Schröder ⋮ Some more properties of Catalan numbers ⋮ Moments on Catalan numbers ⋮ Super ballot numbers ⋮ Skew Dyck paths ⋮ Generalization of a formula of Touchard for Catalan numbers ⋮ Combinatorial proof of certain identities ⋮ A NOTE ON RANDOM MATRIX INTEGRALS, MOMENT IDENTITIES, AND CATALAN NUMBERS ⋮ Pattern avoidance in ``flattened partitions ⋮ Catalan, Motzkin, and Riordan numbers ⋮ Dyck path enumeration

Cites Work

• Über Unterbäume eines Baumes
• A Note on Catalan Parentheses
• Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for non-associative products
• Unnamed Item
• Unnamed Item

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