On the coefficients of power sums of arithmetic progressions

We investigate the coefficients of the polynomialSm,rn(ℓ)=rn+(m+r)n+(2m+r)n+⋯+((ℓ−1)m+r)n. We prove that these can be given in terms of Stirling numbers of the first kind and r-Whitney numbers of the second kind. Moreover, we prove a necessary and sufficient condition for the integrity of these coefficients.