TY - JOUR
TI - The r-Dowling Numbers and Matrices Containing r-Whitney Numbers of the Second Kind and Lah Numbers
PY - 2019/07/25
Y2 - 2024/06/19
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 12
IS - 3
LA - en
DO - 10.29020/nybg.ejpam.v12i3.3494
UR - https://doi.org/10.29020/nybg.ejpam.v12i3.3494
SP - 1122-1137
AB - 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.
ER -