$$U_{263}(x, y) = \frac{1}{\sqrt{1 - 4 x} \left(1 - y\right)}$$

$$T_{263}(n, m, k) = \frac{{\binom{\frac{k}{2} + n - \frac{1}{2}}{n}} {\binom{k + m - 1}{m}} {\binom{k + 2 n - 1}{\frac{k}{2} + n - \frac{1}{2}}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}$$