$$U_{686}(x, y) = \frac{x \left(\sqrt{4 y + 1} + 1\right)}{2} + 1$$

$$T_{686}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} n {\binom{k}{n}} {\binom{2 m - n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$