$$U_{579}(x, y) = \frac{y^{6} \left(4 - 4 \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{4}}{4 y^{8}} + 1}\right)}{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}$$

$$T_{579}(n, m, k) = \frac{k \left(k + 4 n\right) {\binom{k + 2 n - 1}{n}} {\binom{2 k + 2 m + 8 n}{m}}}{\left(k + n\right) \left(k + m + 4 n\right)}$$