Related papers: Poly-Bernoulli Numbers and Eulerian Numbers

We introduce sub-Eulerian polynomials to count elements of $D_n$ by which a recurrence relation for the Eulerian polynomials of type $D$ is obtained.

The Eulerian polynomials enumerate permutations according to their number of descents. We initiate the study of descent polynomials over Cayley permutations, which we call Caylerian polynomials. Some classical results are generalized by…

This paper shows that a finite discrete convolution involving Stirling numbers of both kinds and harmonic numbers can be expressed in terms of the Bernoulli numbers. As applications of this expression, the linear recurrence relation for the…

In this note, we give an alternative proof of the generating function of $p$-Bernoulli numbers. Our argument is based on the Euler's integral representation.

Recently the new q-Euler numbers are defined. In this paper we derive the the Kummer type congruence related to q-Euler numbers and we introduce some interesting formulae related to these q-Euler numbers.

We define and study the combinatorial properties of compositional Bernoulli numbers and polynomials within the framework of rational combinatorics.

We investigate some interesting properties of Bernstein polynomials associated with boson p-adic integrals on Zp.

In this paper, applying the Fa\`a di Bruno formula and some properties of Bell polynomials, several closed formulas and determinantal expressions involving Stirling numbers of the second kind for higher-order Bernoulli and Euler polynomials…

In the paper, the authors establish an explicit formula for computing Bernoulli polynomials at non-negative integer points in terms of $r$-Stirling numbers of the second kind.

For any integer $k$, M.Kaneko defined $k$-th poly-Bernoulli numbers as a kind of generalization of classical Bernoulli numbers using $k$-th polylogarithm. In case when $k$ is positive, $k$-th poly-Bernoulli numbers is a sequence of rational…

In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.

The combinatorial theory for the set of parity alternating permutations is expounded. In view of the numbers of ascents and inversions, several enumerative aspects of the set are investigated. In particular, it is shown that signed Eulerian…

In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.

In this note we present a combinatorial proof of an identity involving poly-Bernoulli numbers and Genocchi numbers. We introduce the combinatorial objects, $m-$barred Callan sequences and show that the identity holds in a more general…

In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.

Eulerian polynomials record the distribution of descents over permutations. Caylerian polynomials likewise record the distribution of descents over Cayley permutations, where a Cayley permutation is a word of positive integers such that if…

In this paper we construct a new q-Euler numbers and polynomials. By using these numbers and polynomials, we give the interesting formulae related to alternating sums of powers of consecutive q-integers following an idea due to Euler.

The aim of this note is to provide a simple proof of some well-known identities and recurrences relating classical Bernoulli and Euler numbers by using the Abel sum of the divergent series $\sum_{n=0}^\infty (-1)^{n} (n+1)^k$, $k$ a…

In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z_p. The methods to study q-Euler numbers and polynomials in this paper are new.

Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on…