Multiple hyperharmonic-star numbers

In a 2022Lithuanian Mathematical Journalarticle, Xu-Zhang-Li intro-duced a remarkable formula for multiple hyperharmonic numbersvia classical multiple harmonic sums. This formula can be extended to the multiple hyperharmonic-star numbers. In this paper, we will show that the multiple hyperharmonic-star numbers H-n ((m))(k(1),...,k(r)) can be expressed in terms of combinations of products of polynomi-als in n of degree at most m-1 and classical multiple harmonic-star sums with depth <= r, and prove that the Euler sums of multiple hyperharmonic-star numbers H-(m)(q;k(1),...,k(r)) can be evaluated by classical multiple zeta-star values with weight <= q;k(1),...,k(r) and depth <= r+1.