Combinatorial Interpretations of the q-Faulhaber and q-Salie   Coefficients
  Recently, Guo and Zeng discovered two families of polynomials featuring in a q-analogue of Faulhaber's formula for the sums of powers and a q-analogue of Gessel-Viennot's formula involving Salie's coefficients for the alternating sums of powers. In this paper, we show that these are polynomials with symmetric, nonnegative integral coefficients by refining Gessel-Viennot's combinatorial interpretations. 
Victor J. W. Guo, Martin Rubey, Jiang Zeng