Two new families of q-positive integers

Let $n,p,k$ be three positive integers. We prove that the rational fractions of $q$: $${\left[\genfrac{}{}{0px}{}{n}{k}\right]}_q{}_3{\varphi }_2[\mathrm{.}matrix{q}^{1-k},q^{-p},q^{p-n}q,q^{1-n}matrix\mathrm{\mid }q;q^{k+1}]\text{and}{q}^{(n-p)p}\text{qbi}nkq{}_3{\varphi }_2[\mathrm{.}matrix{q}^{1-k},q^{-p},q^{p-n}q,q^{1-n}matrix\mathrm{\mid }q;q]$$ are polynomials of $q$ with positive integer coefficients. This generalizes a recent result of Lassalle (Ann. Comb. 6(2002), no. 3-4, 399-405), in the same way as the classical $q$-binomial coefficients refine the ordinary binomial coefficients.