$$U_{1385}(x, y) = \frac{1}{\sqrt{1 - 4 x} \left(1 - y\right)^{2}}$$

$$T_{1385}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0 , k=0} ,\ \\4^{n} {\binom{\frac{k}{2} + n - 1}{n}} {\binom{2 k + m - 1}{m}}&\text{if k even} ,\ \\\frac{{\binom{\frac{k}{2} + n - \frac{1}{2}}{n}} {\binom{k + 2 n - 1}{\frac{k}{2} + n - \frac{1}{2}}} {\binom{2 k + m - 1}{m}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$