The Delannoy polynomial
 |
collects Delannoy numbers along an antidiagonal of their array. Here 
counts lattice paths
from 
to 
with steps 
,
,
and 
(Wang et al. 2019).
The first polynomials are 
, 
, 
, and 
. They satisfy
 |
Their coefficients are symmetric, and all their zeros are negative real numbers (Wang et al. 2019).
Bayer et al. (2026) relate products of these polynomials to face enumeration for independence complexes of planar ternary graphs.
