$$U_{261}(x, y) = x + \frac{1}{\sqrt{1 - 4 y}}$$

$$T_{261}(n, m, k) = \begin{cases}\frac{{\binom{k}{n}} {\binom{\frac{k}{2} + m - \frac{n}{2}}{m}} {\binom{k + 2 m - n}{\frac{k}{2} + m - \frac{n}{2}}}}{{\binom{k - n}{\frac{k}{2} - \frac{n}{2}}}}&\text{if k even} ,\ \\\frac{{\binom{k}{n}} {\binom{\frac{k}{2} + m - \frac{n}{2} - \frac{1}{2}}{m}} {\binom{k + 2 m - n - 1}{\frac{k}{2} + m - \frac{n}{2} - \frac{1}{2}}}}{{\binom{k - n - 1}{\frac{k}{2} - \frac{n}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$