$$U_{262}(x, y) = y + \frac{1}{\sqrt{1 - 4 x}}$$

$$T_{262}(n, m, k) = \begin{cases}\frac{{\binom{k}{m}} {\binom{\frac{k}{2} - \frac{m}{2} + n}{n}} {\binom{k - m + 2 n}{\frac{k}{2} - \frac{m}{2} + n}}}{{\binom{k - m}{\frac{k}{2} - \frac{m}{2}}}}&\text{if k even} ,\ \\\frac{{\binom{k}{m}} {\binom{\frac{k}{2} - \frac{m}{2} + n - \frac{1}{2}}{n}} {\binom{k - m + 2 n - 1}{\frac{k}{2} - \frac{m}{2} + n - \frac{1}{2}}}}{{\binom{k - m - 1}{\frac{k}{2} - \frac{m}{2} - \frac{1}{2}}}}&\text{if k odd} ,\ \\0&\text{if k<m} \end{cases} $$