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
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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.
Share and Cite
ISRP Style
Roberto B. Corcino, Cristina B. Corcino, Jeneveb T. Malusay, A Qi formula for translated \(r\)-Dowling numbers, Journal of Mathematics and Computer Science, 20 (2020), no. 2, 88--100
AMA Style
Corcino Roberto B., Corcino Cristina B., Malusay Jeneveb T., A Qi formula for translated \(r\)-Dowling numbers. J Math Comput SCI-JM. (2020); 20(2):88--100
Chicago/Turabian Style
Corcino, Roberto B., Corcino, Cristina B., Malusay, Jeneveb T.. "A Qi formula for translated \(r\)-Dowling numbers." Journal of Mathematics and Computer Science, 20, no. 2 (2020): 88--100
Keywords
- Qi formula
- Translated \(r\)-Dowling numbers
- Bell polynomials
- Lah numbers
- translated \(r\)-Whitney numbers
- Faa di Bruno's formula
- \(r\)-Whitney-Lah numbers
MSC
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