A Qi formula for translated \(r\)-Dowling numbers

Volume 20, Issue 2, pp 88--100 http://dx.doi.org/10.22436/jmcs.020.02.02
Publication Date: October 19, 2019 Submission Date: June 28, 2019 Revision Date: September 07, 2019 Accteptance Date: September 10, 2019

Authors

Roberto B. Corcino - Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines. Cristina B. Corcino - Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines. Jeneveb T. Malusay - Research Institute for Computational Mathematics and Physics, Cebu Normal University, Osmena Boulevard, Cebu City, Philippines.


Abstract

Another form of an explicit formula for translated \(r\)-Dowling numbers is derived using Faa di Bruno's formula and certain identity of Bell polynomials of the second kind. This formula is expressed in terms of the translated \(r\)-Whitney numbers of the second kind and the ordinary Lah numbers, which is analogous to Qi formula. As a consequence, a relation between translated \(r\)-Dowling numbers and the sums of row entries of the product of two matrices containing the translated \(r\)-Whitney numbers of the second kind and the ordinary Lah numbers is established.


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