Let (P_n) be the Catalan-Larcombe-French numbers. The numbers P_n occur in the theory of elliptic integrals, and are related to the arithmetic-geometric-mean. In this paper we investigate the properties of the related sequence S_n = P_n/2ⁿ instead, since (S_n) is an Apéry-like sequence. We prove a congruence and an inequality for P_n.