$$U_{218}(x, y) = \frac{1 - \sqrt{1 - 4 x}}{2 x \sqrt{1 - 4 y}}$$

$$T_{218}(n, m, k) = \begin{cases}\frac{k {\binom{\frac{k}{2} + m}{m}} {\binom{k + 2 m}{\frac{k}{2} + m}} {\binom{k + 2 n - 1}{n}}}{\left(k + n\right) {\binom{k}{\frac{k}{2}}}}&\text{if k even} ,\ \\\frac{k {\binom{\frac{k}{2} + m - \frac{1}{2}}{m}} {\binom{k + 2 m - 1}{\frac{k}{2} + m - \frac{1}{2}}} {\binom{k + 2 n - 1}{n}}}{\left(k + n\right) {\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$