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Applications of the A. G. M. of Gauss: some new properties of the Catalan-Larcombe-French sequence
... These numbers occur in the theory of elliptic integrals [12], and there are relations to the arithmetic-geometric-mean [10]. The first few P n are 1, 8, 80, 896, 10816, 137728. ...
We develop the Stienstra-Beukers theory of supercongruences in the setting of the Catalan-Larcombe-French sequence. We also give some applications to other sequences. Comment: 14 pages: v2 has improved formatting
In this paper, we discuss the log-behavior of the Catalan–Larcombe–French sequence {Pn}n≥0. We prove that {Pn}n≥0 is log-balanced and {Pn/(n!)2}n≥0 is unimodal. In addition, we show that {Pk/k!}0≤k≤n is reverse ultra log-concave.
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