$$U_{782}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{8 y^{3} \left(- x + \frac{1 - \sqrt{1 - 4 y}}{2 y}\right)^{2}}$$

$$T_{782}(n, m, k) = \begin{cases}{\binom{2 k + n - 1}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - n\right) {\binom{2 k + n - 1}{n}} {\binom{- k - m + n - 1}{m - 1}}}{m} \end{cases} $$