\(p^{q}\)-Catalan numbers and squarefree binomial coefficients

DOI10.1016/S0022-314X(02)00125-7zbMath1021.11002arXivmath/0010148MaRDI QIDQ1394917

Pantelimon Stănică

Publication date: 25 June 2003

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

Full work available at URL: https://arxiv.org/abs/math/0010148

zbMATH Keywords

congruencesbinomial coefficientsgeneralized Catalan numberssquarefree numbers

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65)

Cites Work

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• On divisors of binomial coefficients. I
• A new combinatorial interpretation for generalized Catalan number
• Catalan numbers, their generalization, and their uses
• On generalised Catalan numbers
• Some canonical sequences of integers
• Estimates for the Chebyshev Function ψ(x) - θ(x)
• Some extremal functions in Fourier analysis
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients
• Correspondences between plane trees and binary sequences
• Unsolved problems in number theory

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