Some properties of central Delannoy numbers

In the paper, by investigating the generating function of central Delannoy numbers, the authors establish several explicit expressions, including determinantal expressions, for central Delannoy numbers, present three identities involving the Cauchy products of central Delannoy numbers, discover an integral representation for central Delannoy numbers, find (absolute) monotonicity, convexity, and logarithmic convexity for the sequence of central Delannoy numbers, and construct several product and determinantal inequalities for central Delannoy numbers.