A class of weighted Delannoy numbers

J. M. Grau, A. M Oller-Marcen, J. L. Varona

The weighted Delannoy numbers are defined by the recurrence relation $f_{m,n}=\alpha f_{m-1,n}+\beta f_{m,n-1}+\gamma f_{m-1,n-1}$ if $mn>0$, with $f_{m,n}={\alpha }^m{\beta }^n$ if $nm=0$. In this work, we…