doi:10.2298/FIL2217985GengGrau, JoséOller-Marcén, AntonioVarona, JuanA class of weighted Delannoy numbersART-2022-134847The weighted Delannoy numbers are defined by the recurrence relation fm,n = α fm−1,n +β fm,n−1 + γ fm−1,n−1 if mn > 0, with fm,n = α mβ n if nm = 0. In this work, we study a generalization of these numbers considering the same recurrence relation but with fm,n = A mB n if nm = 0. More particularly, we focus on the diagonal sequence fn,n. With some ingenuity, we are able to make use of well-established methods by Pemantle and Wilson, and by Melczer in order to determine its asymptotic behavior in the case A, B, α, β, γ ≥ 0. In addition, we also study its P-recursivity with the help of symbolic computation tools.2022http://zaguan.unizar.es/record/12772010.2298/FIL2217985Ghttp://zaguan.unizar.es/record/127720oai:zaguan.unizar.es:127720FILOMAT 36, 17 (2022), 5985-6007All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess