Results 51 to 60 of about 427,829 (170)
q-Euler and Genocchi numbers [PDF]
arXiv, 2005 Carlitz has introduced an interesting $q$-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the $q$-Euler numbers. In this paper we give another construction of $q$-Euler numbers, which are different than his $q$-Euler numbers.
arxiv
Multi-Lah numbers and multi-Stirling numbers of the first kind [PDF]
arXiv, 2021 In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm. The aim of this paper is to study several relations among those three numbers.
arxiv
Fibonacci Numbers which are Products of two Pell Numbers [PDF]
The Fibonacci Quarterly, 2016, 2017 In this paper, we find all Fibonacci numbers which are products of two Pell numbers and all Pell numbers which are products of two Fibonacci numbers.
arxiv
On Some Identities and Symmetric Functions for Balancing Numbers
Journal of New Theory, 2018 In this paper, we derivenew generating functions of the product of balancing numbers, Lucas balancingnumbers and the Chebychev polynomials of the second kind by making use ofuseful properties of the symmetric functions mentioned in the paper.
Ali Boussayoud
doaj
Generalized Compositions and Weighted Fibonacci Numbers [PDF]
arXiv, 2010 In this paper we consider particular generalized compositions of a natural number with a given number of parts. Its number is a weighted polynomial coefficient. The number of all generalized compositions of a natural number is a weighted $r$-generalized Fibonacci number. A relationship between these two numbers will be derived. We shall thus obtain a
arxiv
The Super Patalan Numbers [PDF]
J. Integer Seq. 18 (2015), Article 15.3.3, 2014 We introduce the super Patalan numbers, a generalization of the super Catalan numbers in the sense of Gessel, and prove a number of properties analagous to those of the super Catalan numbers. The super Patalan numbers generalize the super Catalan numbers similarly to how the Patalan numbers generalize the Catalan numbers.
arxiv
Continued fraction expansions of the generating functions of Bernoulli and related numbers [PDF]
arXiv, 2019 We give continued fraction expansions of the generating functions of Bernoulli numbers, Cauchy numbers, Euler numbers, harmonic numbers, and their generalized or related numbers. In particular, we focus on explicit forms of the convergents of these continued fraction expansions.
arxiv
Some Congruences for Balancing and Lucas-Balancing Numbers and Their Applications
, 2014 See the abstract in the attached pdf.
openaire +2 more sources
Remarks on hypergeometric Cauchy numbers [PDF]
arXiv, 2018 Hypergeometric numbers can be recognized as one of the most natural extensions of the classical Cauchy numbers in terms of determinants, though many kinds of generalizations of the Cauchy numbers have been considered by many authors. In addition, there are some relations between the hypergeometric Cauchy numbers and the classical Cauchy numbers.
arxiv
Arithmetic properties of q-Fibonacci numbers and q-Pell numbers [PDF]
arXiv, 2005 We investigate some arithmetic properties of the q-Fibonacci numbers and the q-Pell numbers.
arxiv