On an upper bound for central binomial coefficients and Catalan numbers

2024/07/27 by Jean‐Christophe Pain, Pain, Jean-Christophe
Mathematics · #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2407.21064

openalex publication_date 2024/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently, Agievich proposed an interesting upper bound on binomial coefficients in the de Moivre-Laplace form. In this article, we show that the latter bound, in the specific case of a central binomial coefficient, is larger than the one proposed by Sasvari and obtained using the Binet formula for the Gamma function. In addition, we provide the expression of the next-order bound and apply it to Catalan numbers C_n. The bounds are very close to the exact value, the difference decreasing with n and with the order of the upper bound.

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