Hankel determinants for generating functions of Catalan-like numbers. Issue 3 (4th March 2019) - Liu, Lily Li; Mu, Lili
Abstract: LetR n ( x ) = ∑ i = 0 n r i x n - i be the generating functions of Catalan-like numbers( r n ) n ≥ 0 . We show that the corresponding Hankel determinantsdet [ R i + j ( x ) ] 0 ≤ i, j ≤ n satisfy a three-term recurrence relation. As applications, we express the Hankel determinants of some classical combinatorial counting coefficients, including the Catalan numbers, the central binomial coefficients, the large and little Schröder numbers, in a unified way.