$$U_{217}(x, y) = \frac{1}{\left(1 - x\right)^{2} \sqrt{1 - 4 y}}$$

$$T_{217}(n, m, k) = \begin{cases}\frac{{\binom{\frac{k}{2} + m}{m}} {\binom{k + 2 m}{\frac{k}{2} + m}} {\binom{2 k + n - 1}{n}}}{{\binom{k}{\frac{k}{2}}}}&\text{if k even} ,\ \\\frac{{\binom{\frac{k}{2} + m - \frac{1}{2}}{m}} {\binom{k + 2 m - 1}{\frac{k}{2} + m - \frac{1}{2}}} {\binom{2 k + n - 1}{n}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$