Some Determinants Involving Incomplete Fubini Numbers

[1] M. Aoki and T. Komatsu, Remarks on hypergeometric Bernoulli numbers, preprint.Search in Google Scholar

[2] M. Aoki and T. Komatsu, Remarks on hypergeometric Cauchy numbers, Math. Rep. (Bucur.), to appear. arXiv:1802.05455Search in Google Scholar

[3] M. Bona and I. Mező, Real zeros and partitions without singleton blocks, European J. Combin., 51 (2016), 500–510.10.1016/j.ejc.2015.07.021Search in Google Scholar

[4] D. Bozkurt and T.-Y. Tam, Determinants and inverses of r-circulant matrices associated with a number sequence, Linear Multilinear Algebra 63(10) (2015), 2079–2088.10.1080/03081087.2014.941291Search in Google Scholar

[5] F. Brioschi, Sulle funzioni Bernoulliane ed Euleriane, Annali de Mat., i. (1858), 260–263; Opere Mat., i. pp. 343–347.10.1007/BF03197335Search in Google Scholar

[6] J. Y. Choi and J. D. H. Smith, Reciprocity for multi-restricted numbers, J. Combin. Theory Ser. A, 113(2006), 1050–1060.10.1016/j.jcta.2005.10.001Search in Google Scholar

[7] L. Comtet. Advanced Combinatorics. D. Reidel Publishing Co. (Dordrecht, Holland), 1974.10.1007/978-94-010-2196-8Search in Google Scholar

[8] J. W. L. Glaisher, Expressions for Laplace’s coefficients, Bernoullian and Eulerian numbers etc. as determinants, Messenger (2) 6 (1875), 49–63.Search in Google Scholar

[9] T. Komatsu, Incomplete poly-Cauchy numbers, Monatsh. Math. 180 (2016), 271–288.10.1007/s00605-015-0810-zSearch in Google Scholar

[10] T. Komatsu, K. Liptai and I. Mező, Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers, Publ. Math. Debrecen 88 (2016), 357–368.10.5486/PMD.2016.7361Search in Google Scholar

[11] T. Komatsu, I. Mező and L. Szalay, Incomplete Cauchy numbers, Acta Math. Hungar. 149 (2016), 306–323.10.1007/s10474-016-0616-zSearch in Google Scholar

[12] T. Komatsu and J. L. Ramírez, Generalized poly-Cauchy and poly-Bernoulli numbers by using incomplete r-Stirling numbers, Aequationes Math. 91(2017), 1055–1071.10.1007/s00010-017-0509-4Search in Google Scholar

[13] T. Komatsu and P. Yuan, Hypergeometric Cauchy numbers and polynomials, Acta Math. Hungar. 153 (2017), 382–400.10.1007/s10474-017-0744-0Search in Google Scholar

[14] H. Li and T. MacHenry, Permanents and determinants, weighted isobaric polynomials, and integer sequences, J. Integer Seq. 16(2013), Article 13.3.5.Search in Google Scholar

[15] H.-C. Li, On Fibonacci-Hessenberg matrices and the Pell and Perrin numbers, Appl. Math. Comput. 218 (17) (2012), 8353–8358.10.1016/j.amc.2012.01.062Search in Google Scholar

[16] T. Mansour and M. Schork. Commutations Relations, Normal Ordering, and Stirling numbers. CRC Press, 2015.10.1201/b18869Search in Google Scholar

[17] D. Merlini, R. Sprugnoli and M. C. Verri, The Cauchy numbers, Discrete Math. 306, 1906–1920.10.1016/j.disc.2006.03.065Search in Google Scholar

[18] I. Mező, Periodicity of the last digits of some combinatorial sequences, J. Integer Seq. 17 (2014), Article 14.1.1.Search in Google Scholar

[19] I. Mező and J. L. Ramírez, The linear algebra of the r-Whitney matrices, Integral Transforms Spec. Funct. 26(3) (2015), 213–225.10.1080/10652469.2014.984180Search in Google Scholar

[20] V. Moll, J. L. Ramírez, and D. Villamizar. Combinatorial and arithmetical properties of the restricted and associated Bell and factorial numbers, J. Comb., To appear.Search in Google Scholar

[21] T. Muir, The theory of determinants in the historical order of development, Four volumes, Dover Publications, New York, 1960.Search in Google Scholar

[22] OEIS Foundation Inc. (2017), The on-line encyclopedia of integer sequences, available at https://oeis.org/.Search in Google Scholar

[23] A. Şahin and J. L. Ramírez, Determinantal and permanental representations of convolved Lucas polynomials, Appl. Math Comput. 281 (2016), 314–322.10.1016/j.amc.2016.01.064Search in Google Scholar

[24] P. Tang and A. Xu, Divided differences and a unified approach to evaluating determinants involving generalized factorials, Linear Multilinear Algebra 61(1) (2013), 59–71.10.1080/03081087.2012.663369Search in Google Scholar

[25] N. Trudi, Intorno ad alcune formole di sviluppo, Rendic. dell’ Accad. Napoli, (1862), 135–143.Search in Google Scholar

[26] A. Xu and T. Zhou, Some identities related to the r-Whitney numbers, Integral Transforms Spec. Funct. 27(11) (2016), 920–929.10.1080/10652469.2016.1229316Search in Google Scholar

[27] F. Yilmaz and D. Bozkurt, Hessenberg matrices and the Pell and Perrin numbers, J. Number Theory 131(8) (2011), 1390–1396.10.1016/j.jnt.2011.02.002Search in Google Scholar