Conjectures involving a generalization of the sums of powers of integers

TL;DR

This paper explores a broad class of sums extending the sums of powers of integers, proposing several conjectures about their representations to advance understanding in this mathematical area.

Contribution

It introduces a generalized framework for sums of powers and formulates new conjectures about their properties and representations.

Findings

Proposes multiple conjectures on sum representations

Extends classical sums of powers to a broader class

Provides a foundation for future proof efforts

Abstract

Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.