$$U_{679}(x, y) = \frac{1 - \sqrt{\frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1}}{2 x}$$

$$T_{679}(n, m, k) = \frac{\left(-1\right)^{k + n} k {\binom{k + 2 n - 1}{k + n - 1}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$