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Sun defined a new kind of refined Eulerian polynomials, namely, \\begin{eqnarray*} A_n(p,q)=\\sum_{\\pi\\in \\mathfrak{S}_n}p^{{\\rm odes}(\\pi)}q^{{\\rm edes}(\\pi)} \\end{eqnarray*} for $n\\geq 1$, where ${odes}(\\pi)$ and ${edes}(\\pi)$ enumerate the number of descents of permutation $\\pi$ in odd and even positions, respectively. In this paper, we build an exponential generating function for $A_{n}(p,q)$ and establish an explicit formula for $A_{n}(p,q)$ in terms of Eulerian polynomials $A_{n}(q)$ and $C(q)$, the generating function for Catalan numbers. 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