Moments on Catalan numbers

DOI10.1016/j.jmaa.2008.08.042zbMath1168.11004OpenAlexW2061798431MaRDI QIDQ953493

Xiaojing Chen, Chu, Wenchang

Publication date: 6 November 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.08.042

zbMATH Keywords

Catalan numberstelescoping methodChu-Vandermonde convolution

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65)

Related Items

Moments on quadratic binomial products, Unnamed Item, Catalan generating functions for bounded operators, Some new binomial sums related to the Catalan triangle, Powers of Catalan generating functions for bounded operators, Minors of a class of Riordan arrays related to weighted partial Motzkin paths, Sums of powers of Catalan triangle numbers, Moments of combinatorial and Catalan numbers, Proofs of two conjectures on Catalan triangle numbers, Combinatorial identities related to \(2 \times 2\) submatrices of recursive matrices, FACTORS OF SUMS AND ALTERNATING SUMS INVOLVING BINOMIAL COEFFICIENTS AND POWERS OF INTEGERS, Ballot matrix as Catalan matrix power and related identities, Factors of binomial sums from the Catalan triangle, Triple product sums of Catalan triangle numbers

Cites Work

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• Catalan numbers, their generalization, and their uses
• A Catalan triangle
• A short proof of an identity of Touchard's concerning Catalan numbers
• Generalization of a formula of Touchard for Catalan numbers
• Catalan-like numbers and determinants
• New identities in the Catalan triangle
• Divided differences and generalized Taylor series
• A Note on Catalan Parentheses