Abstract
The Delannoy numbers d(n,k) count the number of lattice paths from (0,0) to (n−k,k) using steps (1,0),(0,1) and (1,1). We show that the zeros of all Delannoy polynomials dn(x)=∑k=0nd(n,k)xk are in the open interval (−3−22,−3+22) and are dense in the corresponding closed interval. We also show that the Delannoy numbers d(n,k) are asymptotically normal (by central and local limit theorems).
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