Representations of Various Power Sums

We give new representations of various power sums, including the signed/alternating sum of powers of consecutive integers as well as odd numbers. The generalized Eulerian power sums \(E_{n,m}(z):=\sum _{k=1}^n k^mz^k\) $E_{n,m}(z):={\sum }_{k=1}^n{k}^m{z}^k$ are also considered.