Geodesic
Two properties of Catalan-Larcombe-French numbers
Journal of integer sequences, Tome 19 (2016) no. 3
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 $S_{n} = P_{n}/2^{n}$ instead, since $(S_{n})$ is an Apéry-like sequence. We prove a congruence and an inequality for $P_{$n$.$
Classification : 11A07, 05A10, 05A19, 05A20
Keywords: congruence, inequality, Catalan-larcombe-French number 
@article{JIS_2016__19_3_a2,
     author = {Ji,  Xiao-Juan and Sun,  Zhi-Hong},
     title = {Two properties of {Catalan-Larcombe-French} numbers},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {3},
     zbl = {1415.11010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_3_a2/}
}
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Ji,  Xiao-Juan; Sun,  Zhi-Hong. Two properties of Catalan-Larcombe-French numbers. Journal of integer sequences, Tome 19 (2016) no. 3. http://geodesic.mathdoc.fr/item/JIS_2016__19_3_a2/