Geodesic
Hankel transforms of linear combinations of Catalan numbers
Journal of integer sequences, Tome 14 (2011) no. 5
Cvetković, Rajković, and Ivković proved that the Hankel transform of the sequence of sums of adjacent Catalan numbers is the bisection of the sequence of Fibonacci numbers. Here, we find recurrence relations for the Hankel transform of more general linear combinations of Catalan numbers, involving up to four adjacent Catalan numbers, with arbitrary coefficients. Using these, we make certain conjectures about the recurrence relations satisfied by the Hankel transform of more extended linear combinations.
Classification : 11C20, 11B37, 11B75, 15A15
Keywords: Hankel transform, Catalan numbers, recurrence relations, integer sequences 
@article{JIS_2011__14_5_a7,
     author = {Dougherty,  Michael and French,  Christopher and Saderholm,  Benjamin and Qian,  Wenyang},
     title = {Hankel transforms of linear combinations of {Catalan} numbers},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {5},
     zbl = {1232.11036},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_5_a7/}
}
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%A Qian,  Wenyang
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Dougherty,  Michael; French,  Christopher; Saderholm,  Benjamin; Qian,  Wenyang. Hankel transforms of linear combinations of Catalan numbers. Journal of integer sequences, Tome 14 (2011) no. 5. http://geodesic.mathdoc.fr/item/JIS_2011__14_5_a7/