Generalized Bessel numbers and some combinatorial settings

Combinatorial Interpretation of Generalized Stirling Numbers

A combinatorial interpretation of the earlier studied generalized Stirling numbers, emerging in a normal ordering problem and its inversion, is given. It involves unordered forests of certain types of labeled trees. Partition number arrays related to such forests are also presented.

Combinatorial Representation of Generalized Fibonacci Numbers

New formull are presented which express various generalizations of Fibonacci numbers as simple sums of binomial and multinomial coeecients. The equalities are inferred from the special properties of the representations of the integers in certain numeration systems.

Some summation formulas involving harmonic numbers and generalized harmonic numbers

Identities Involving Generalized Harmonic Numbers and Other Special Combinatorial Sequences

In this paper, we study the properties of the generalized harmonic numbersHn,k,r(α, β). In particular, by means of the method of coefficients, generating functions and Riordan arrays, we establish some identities involving the numbers Hn,k,r(α, β), Cauchy numbers, generalized Stirling numbers, Genocchi numbers and higher order Bernoulli numbers. Furthermore, we obtain the asymptotic values of s...

Explicit Formulas and Combinatorial Identities for Generalized Stirling Numbers

In this paper, a modified approach to the multiparameter non-central Stirling numbers via differential operators, introduced by El-Desouky, and new explicit formulae of both kinds of these numbers are given. Also, some relations between these numbers and the generalized Hermite and Truesdel polynomials are obtained. Moreover, we investigate some new results for the generalized Stirling-type pai...