New formulas for Stirling-like numbers and Dobinski-like formulas

TL;DR

This paper introduces new formulas extending Stirling-like numbers and Dobinski-like formulas, including q-extensions, contributing to combinatorial mathematics and its foundational aspects in computer science.

Contribution

It proposes novel extensions of Stirling and Dobinski formulas, encompassing known q-extensions, with applications in the foundations of computer science.

Findings

New formulas for Stirling-like numbers introduced

Dobinski-like formulas extended with new variants

Includes q-extensions as part of the generalization

Abstract

Extensions of the $Stirling$ numbers of the second kind and $Dobinski$ -like formulas are proposed in a series of exercises for graduates. Some of these new formulas recently discovered by me are to be found in the source paper $ [1]$. These extensions naturally encompass the well known $q$- extensions. The indicatory references are to point at a part of the vast domain of the foundations of computer science in arxiv affiliation.