$$U_{685}(x, y) = \frac{1 - \sqrt{\frac{2 x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{y^{2}} + 1}}{2 x}$$

$$T_{685}(n, m, k) = \frac{\left(-1\right)^{- k + n} k {\binom{k + 2 n - 1}{k + n - 1}} {\binom{2 k + 2 m + 2 n}{m}}}{k + m + n}$$