$$U_{807}(x, y) = \frac{y^{2} \left(- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} - 2 \sqrt{- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1} + 2\right)}{x^{2} \left(1 - \sqrt{1 - 4 y}\right)^{2}}$$

$$T_{807}(n, m, k) = \begin{cases}\frac{k n {\binom{2 k + 2 n}{n}} {\binom{2 m + n - 1}{m}}}{\left(k + n\right) \left(m + n\right)},\ \\1&\text{if n=0,m=0} \end{cases} $$