On Some Identities Involving Cauchy Products of Central Delannoy Numbers

Year 2021, , 3063 - 3071, 15.12.2021

Serpil Halıcı

https://doi.org/10.21597/jist.937483

Abstract

In this paper, we have examined Cauchy products of central Delannoy numbers. Moreover, using their recurrence relation we have derived some important identities such as the Cassini and Catalan's identities which contain these products.

Keywords

Recurrences, Cauchy Products, Delannoy numbers, identities

Project Number

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References

• Badri M, Szeptycki P, 1990. Cauchy Products of Positive Sequences, The Rocky Mountain Journal of Mathematics, 20(2), 351-357.
• Banderier C, and Schwer S, 2005. Why Delannoy numbers?, Journal of Statistical Planning and Inference, 135(1), 40-54.
• Deveci O, Shannon A. G, 2021. Some Aspects of Neyman Triangles and Delannoy Arrays, Mathematica Montisnigri, 1, 36-43.
• Hetyei G., 2006. Central Delannoy numbers and balanced Cohen-Macaulay complexes, Annals of Combinatorics, 10(4), 443-462.
• Qi F, Cernanova V, Shi XT, and Guo B.N, 2018. Some properties of central Delannoy numbers, J. Comput. Appl. Math., 328, 101-115.
• Qi F, Cernanova V, and Y. S. Semenov, 2019. Some tridiagonal determinants related to central Delannoy numbers, the Chebyshev polynomials, and the Fibonacci polynomials, Politehn. Univ. Bucharest Sci. Bull. Ser. A. Appl. Math. Phys, 81(1), 123-136.
• Qi F, B. N. Guo, V. Cernanova and Shi XT, 2016. Explicit expressions, Cauchy products, integral representations, convexity, and inequalities of central Delannoy numbers, ResearchGate preprint, available online at http://dx.doi.org/10.13140/RG.2.1.4889.6886.
• Sulanke RA, 2003. Objects counted by the central Delannoy numbers, J. Integer Seq., 6(1).
• Wang Y, Zheng SN, and X. Chen, 2019. Analytic aspects of Delannoy numbers, Discrete Mathematics, 42(8), 2270-2277.