Half of a Riordan array and restricted lattice paths

For an infinite lower triangular matrix G = (g(n,k))(n,k >= 0), we define the half of G to be the infinite lower triangular matrix H = (h(n,k))(n,k >= 0) such that h(n,k) = g(2n-k,n) for all n >= k >= 0. In this paper, we will show that if G = (g(n,k))(n,k >= 0) is a Riordan array, then its half H = (h(n,k))(n,k >= 0) is also a Riordan array, and we obtain new combinatorial interpretations for some Riordan arrays in terms of weighted lattice paths. (C) 2017 Elsevier Inc. All rights reserved.