Geodesic
A class of weighted Delannoy numbers
Filomat, Tome 36 (2022) no. 17, p. 5985

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DOI

The weighted Delannoy numbers are defined by the recurrence relation f m,n = α f m−1,n + β f m,n−1 + γ f m−1,n−1 if mn > 0, with f m,n = α m β n if nm = 0. In this work, we study a generalization of these numbers considering the same recurrence relation but with f m,n = A m B n if nm = 0. More particularly, we focus on the diagonal sequence f n,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.
DOI : 10.2298/FIL2217985G
Classification : 11B75, 11B37, 05A15, 05A16
Keywords: Delannoy numbers, weighted Delannoy numbers, generating functions, asymptotics 
José María Grau; Antonio M Oller-Marcén; Juan Luis Varona. A class of weighted Delannoy numbers. Filomat, Tome 36 (2022) no. 17, p. 5985 . doi: 10.2298/FIL2217985G
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     title = {A class of weighted {Delannoy} numbers},
     journal = {Filomat},
     pages = {5985 },
     year = {2022},
     volume = {36},
     number = {17},
     doi = {10.2298/FIL2217985G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2217985G/}
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