$$U_{701}(x, y) = \frac{1}{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{2 y} + 1}$$

$$T_{701}(n, m, k) = \begin{cases}1&\text{if n+m=0} ,\ \\\frac{n {\binom{2 m + 2 n}{m}} {\binom{k + n - 1}{n}}}{m + n} \end{cases} $$