Journal of Integer Sequences, Vol. 19 (2016), Article 16.3.4

Two Properties of Catalan-Larcombe-French Numbers

Xiao-Juan Ji
School of Mathematical Sciences
Soochow University
Jiangsu 215006
P. R. China

Zhi-Hong Sun
School of Mathematical Sciences
Huaiyin Normal University
Jiangsu 223001
P. R. China


Let (Pn) be the Catalan-Larcombe-French numbers. The numbers Pn 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 Sn = Pn/2n instead, since (Sn) is an Apéry-like sequence. We prove a congruence and an inequality for Pn.

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(Concerned with sequence A053175.)

Received November 21 2015; revised versions received November 24 2015; February 23 2016. Published in Journal of Integer Sequences, April 6 2016.

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