Moments of combinatorial and Catalan numbers

DOI10.1016/j.jnt.2010.01.018zbMath1214.11033OpenAlexW1993530625MaRDI QIDQ982537

Natalia Romero, Pedro José Miana

Publication date: 7 July 2010

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.01.018

zbMATH Keywords

combinatorial identitiesbinomial coefficientsCatalan numbers

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68)

Related Items (13)

Moments on quadratic binomial products ⋮ 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 ⋮ Factors of sums and alternating sums of products of \(q\)-binomial coefficients and powers of \(q\)-integers ⋮ Reduction formula of a double binomial sum ⋮ Sums of powers of Catalan triangle numbers ⋮ Proofs of two conjectures on Catalan triangle numbers ⋮ Combinatorial identities related to \(2 \times 2\) submatrices of recursive matrices ⋮ A note on the moments of the Kesten distribution ⋮ FACTORS OF SUMS AND ALTERNATING SUMS INVOLVING BINOMIAL COEFFICIENTS AND POWERS OF INTEGERS ⋮ A semicircle law and decorrelation phenomena for iterated Kolmogorov loops

Cites Work

• Moments on Catalan numbers
• Factors of binomial sums from the Catalan triangle
• Catalan numbers, their generalization, and their uses
• A Catalan triangle
• New identities in the Catalan triangle
• Rational Functions Certify Combinatorial Identities
• Divided differences and generalized Taylor series
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