相关论文: Hankel determinants of Schroeder-like numbers

I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.

Recently I. Mezo studied a simple but interesting generalization of the exponential polynomials. In this note I consider two q-analogues of these polynomials and compute their Hankel determinants.

We give simple proofs for the Hankel determinants of q-exponential polynomials.

In this (mostly expository) paper I want to share some observations prompted by a class of matrices whose determinants are Catalan numbers. Considering different methods of proof we obtain some generalizations and q-analogues and…

In this paper we shall survey the various methods of evaluating Hankel determinants and as an illustration we evaluate some Hankel determinants of a q-analogue of Catalan numbers. Here we consider $\frac{(aq;q)_{n}}{(abq^{2};q)_{n}}$ as a…

This note presents some results about Hankel determinants of backwards shifted Catalan-like numbers and related sequences.

In this note we show that various natural q-analogues of the Catalan numbers can be obtained in a uniform way. Furthermore we compute their Hankel determinants.

In this (partly expository) paper we give a short overview about the close relationship between the sequence of Catalan numbers and Hankel determinants from the point of view of orthogonal polynomials and show that an analogous situation…

I study Hankel determinants of a class of sequences which can be interpreted as generalizations of the Catalan numbers and the central binomial coefficients. They follow a modular pattern with a frequent appearance of zeroes, so that the…

We give an overview of known results about Hilbert matrices from the point of view of orthogonal polynomials and compute Hankel determinants of harmonic numbers and related topics.

In this paper we introduce a class of determinants "of Hankel type". We use them to compute certain remarkable families of Drinfeld quasi-modular forms.

We evaluate the Hankel determinants of various sequences related to Bernoulli and Euler numbers and special values of the corresponding polynomials. Some of these results arise as special cases of Hankel determinants of certain sums and…

We consider Hankel determinants of the sequence of Catalan numbers modulo 2 (interpreted as integers 0 and 1) and more generally Hankel determinants where the sum over all permutations reduces to a single signed permutation.

Starting with some determinants of binomial coefficients which are related to Fibonacci and Lucas polynomials we study similar determinants for some generalizations of these polynomials and their q-analogues.

This note gives a simple approach to q-analogues of some results associated with Abel polynomials.

A new $q$-analogue of Appell polynomial sequences and their generalizations are introduced and their main characterizations are proved. As consequences new $q$-analogue of Bernoulli and Euler polynomials and numbers is introduced, their…

Computer experiments suggest some conjectures about Hankel determinants of convolution powers of Catalan numbers. Unfortunately, for most of them I have no proofs. I would like to present them anyway hoping that someone finds them…

We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.

Carlitz has introduced q-analogues of the Bernoulli numbers around 1950. We obtain a representation of these q-Bernoulli numbers (and some shifted version) as moments of some orthogonal polynomials. This also gives factorisations of Hankel…

The middle binomial coefficients can be interpreted as numbers of Motzkin paths which have no horizontal steps at positive heights. Assigning suitable weights gives some nice polynomial extensions. We determine the Hankel determinants and…