@article{The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers_2019, place={Maryland, USA}, volume={12}, url={https://www.ejpam.com/index.php/ejpam/article/view/3494}, DOI={10.29020/nybg.ejpam.v12i3.3494}, abstractNote={This paper derives another form of explicit formula for $(r,\beta)$-Bell numbers using the Faa di Bruno's formula and certain identity of Bell polynomials of the second kind. This formula is expressed in terms Â of the $r$-Whitney numbers of the second kind and the ordinary Lah numbers. As a consequence, a relation between $(r,\beta)$-Bell numbers and the sums of row entries of the product of two matrices containing the $r$-Whitney numbers of the second kind and the ordinary Lah numbers is established. Â Moreover, a $q$-analogue of the explicit formula is obtained.}, number={3}, journal={European Journal of Pure and Applied Mathematics}, year={2019}, month={Jul.}, pages={1122–1137} }