Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-21T03:57:42.805Z Has data issue: false hasContentIssue false


Published online by Cambridge University Press:  07 June 2021

School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), PR China and Current address: Department of Mathematics and Physics, University of Salento (P. O. Box 193), 73100 Lecce, Italy


By making use of the Cauchy double alternant and the Laplace expansion formula, we establish two closed formulae for the determinants of factorial fractions that are then utilised to evaluate several determinants of binomial coefficients and Catalan numbers, including those obtained recently by Chammam [‘Generalized harmonic numbers, Jacobi numbers and a Hankel determinant evaluation’, Integral Transforms Spec. Funct. 30(7) (2019), 581–593].

Research Article
© 2021 Australian Mathematical Publishing Association Inc.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Aigner, M., ‘Catalan-like numbers and determinants’,J. Combin. Theory Ser. A 87 (1999), 3351.CrossRefGoogle Scholar
Aigner, M., ‘Catalan and other numbers: a recurrent theme’, in: Algebraic Combinatorics and Computer Science (eds. Crapo, H. and Senato, D.) (Springer, Milan, 2001), 347390.CrossRefGoogle Scholar
Amdeberhan, T. and Zeilberger, D., ‘Determinants through the looking glass’,Adv. Appl. Math. 27 (2001), 225230.CrossRefGoogle Scholar
Burchnall, J. L., ‘Some determinants with hypergeometric elements’, Q. J. Math. 3 (1952), 151157.CrossRefGoogle Scholar
Chammam, W., ‘Generalized harmonic numbers, Jacobi numbers and a Hankel determinant evaluation’,Integral Transforms Spec. Funct. 30(7) (2019), 581593.CrossRefGoogle Scholar
Chu, W., ‘Inversion techniques and combinatorial identities: a quick introduction to hypergeometric evaluations’,Math. Appl. 283 (1994), 3157.Google Scholar
Chu, W., ‘Divided differences and symmetric functions’,Boll. Unione Mat. Ital. 2-B(3) (1999), 609618.Google Scholar
Chu, W., ‘Binomial convolutions and determinant identities’,Discrete Math. 204(1–3) (1999), 129153.CrossRefGoogle Scholar
Chu, W., ‘Generalizations of the Cauchy determinant’,Publ. Math. Debrecen 58(3) (2001), 353365.Google Scholar
Chu, W., ‘The Cauchy double alternant and divided differences’,Electron. J. Linear Algebra 15 (2006), 1421.CrossRefGoogle Scholar
Chu, W., ‘Finite differences and determinant identities’,Linear Algebra Appl. 430(1) (2009), 215228.Google Scholar
Chu, W., ‘Telescopic generalizations for two 3 F 2-series identities’,Math. Slovaca 62(4) (2012), 689694.CrossRefGoogle Scholar
Gould, H. W. and Hsu, L. C., ‘Some new inverse series relations’,Duke Math. J. 40 (1973), 885891.CrossRefGoogle Scholar
Ostrowski, A. M., ‘On some determinants with combinatorial numbers,J. reine angew. Math. 216 (1964), 2530.CrossRefGoogle Scholar
Tamm, U., ‘Some aspects of Hankel matrices in coding theory’,Electron. J. Combin. 8 (2001), Article ID #A1.CrossRefGoogle Scholar