On an upper bound for central binomial coefficients and Catalan numbers
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910548021477376 |
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| author | Pain, Jean-Christophe |
| author_facet | Pain, Jean-Christophe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On an upper bound for central binomial coefficients and Catalan numbers Pain, Jean-Christophe Combinatorics 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. |
| title | On an upper bound for central binomial coefficients and Catalan numbers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.21064 |