The asymptotic behaviour of the catalan-larcombe-french sequence {1, 8, 80, 896, 10816, . . .}

Abstract

This sequence was discussed at length in a previous article by Larcombe and French, having arisen originally in a historical formulation by E.C. Catalan. The following short paper presents an analysis of the asymptotic behaviour of the sequence, which also naturally generates the asymptotic form of two associated hypergeometric functions.