For positive integers N and M, the general hypergeometric Cauchy polynomials c M, N, n
(z)(M, N≥ 1; n≥ 0) are defined by 1 (1+ t)^ z 1 _2F_1 (M, N; N+ 1;-t)= n= 0^ ∞ c_ M, N, n …

Using the language of runs and patterns, a peak in a sequence of integers can be
interpreted as observing a fall (or descent) immediately after a rise (or ascent). In this paper …

We give continued fraction expansions of the generating functions of Bernoulli numbers,
Cauchy numbers, Euler numbers, harmonic numbers, and their generalized or related …

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 …

For an integer $ k $, define poly-Euler numbers of the second kind $\widehat E_n^{(k)} $($
n= 0, 1,\dots $) by $$\frac {{\rm Li} _k (1-e^{-4 t})}{4\sinh t}=\sum_ {n= 0}^\infty\widehat …

where ω is a complex root of x2+ x+ 1= 0. In 1875, Glaisher gave several interesting
determinant expressions of numbers, including Bernoulli and Euler numbers. These …

Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers Page 1 Beáta
BÉNYI et Toshiki MATSUSAKA Combinatorial aspects of poly-Bernoulli polynomials and …

In this paper, we introduce the higher order hypergeometric Euler numbers and show
several interesting expressions. In 1875, Glaisher gave several interesting determinant …

By studying Cameron's operator in terms of determinants, two kinds of “integer” sequences
of incomplete numbers were introduced. One was the sequence of restricted numbers …

In this paper, we introduce the truncated Euler-Carlitz numbers as analogues of
hypergeometric Euler numbers. In a special case, Euler-Carlitz numbers are defined, which …