Related papers: Some integral representations and properties of La…
In this paper, we introduce the Lah-Bell numbers and their natural extensions, namely the Lah-Bell polynomials, and derive some basic properties of such numbers and polynomials by using elementary methods. In addition, we consider the…
In the paper, utilizing respectively the induction, a generating function of the Lah numbers, the Chu-Vandermonde summation formula, an inversion formula, the Gauss hypergeometric series, and two generating functions of the Stirling numbers…
We present various identities in the form of convolutions involving Stirling numbers of both kinds, Lah numbers, and binomial coefficients. Certain convolution polynomials are discussed also. The proofs are based on several series…
In this paper, we study various properties of matroidal ideals.
In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind.
In this paper we investigate some divisibility properties of Jacobsthal numbers.
We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the r-Stirling and r-Lah numbers are also given. For all these…
We consider random fields admitting a spectral representation with infinitely divisible integrator and prove some of their properties.
We provide a combinatorial interpretation of Lah numbers by means of planar networks. Henceforth, as a conesquence of Lindstr\"om's lemma, we conclude that the related Lah matrix possesses a remarkable property of total non-negativity.
We introduce numerical characteristics of Sylvester and Hadamard matrices and give their estimates and some of their applications.
We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
In this paper we introduce and study two generalizations of Lah numbers, analogous to the Stirling numbers with higher level - a combinatorial one (Lah numbers with higher level) and an algebraic one (Lah numbers of order $s$). We define…
In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
Logarithmic integrals revisited. We consider integrals of the form $\int_0^1 \ln{\ln{(\frac{1}{x})}}R{(x)}{\rm d}x$ again, where $R{(x)}$ is a rational function, and we will explain a way to obtain their values.
We give a survey of the Lagrange inversion formula, including different versions and proofs, with applications to combinatorial and formal power series identities.
In this note, we introduce arithmetic Heilbronn supercharacters that generalize the notions of arithmetic Heilbronn characters and Heilbronn supercharacters and discuss several properties of them.
The author has constructed multiple analogues of several families of combinatorial numbers in a recent article, including the bracket symbol, and the Stirling numbers of the first and second kind. In the present paper, a multiple analogue…
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Lah numbers and Stirling numbers of the second kind.