Mathematics is the science of patterns, and mathematicians attempt to understand these
patterns and discover new ones using a variety of tools. In Proofs That Really Count, award …

In this note we show that a seemingly new class of Stirling-type pairs can be applied to
produce a new representation of the Bernoulli polynomials at positive rational arguments. A …

The r-Lah numbers - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals &
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Combinatorics and Number Theory of Counting Sequences is an introduction to the theory
of finite set partitions and to the enumeration of cycle decompositions of permutations. The …

In this work, we introduce a symmetric algorithm obtained by the recurrence relation ank= an-
1k+ ank-1. We point out that this algorithm can be applied to hyperharmonic-, ordinary and …

By observing that the infinite triangle obtained from some generalized harmonic numbers
follows a Riordan array, we obtain very simple connections between the Stirling numbers of …

The first five harmonic numbers are H1= 1, H2= 3/2, H3= 11/6, H4= 25/12, H5= 137/60. For
convenience we define H0= 0. Since the harmonic series diverges, Hn can get arbitrarily …

We show that the sum of the series formed by the so-called hyperharmonic numbers can be
expressed in terms of the Riemann zeta function. These results enable us to reformulate …

In this paper, polynomials whose coefficients involve r-Lah numbers are used to evaluate
several summation formulae involving binomial coefficients, Stirling numbers, harmonic or …

The hyperharmonic numbers hn (r) are defined by means of the classical harmonic
numbers. We show that the Euler-type sums with hyperharmonic numbers: σ (r, m)=∑ n …