$$U_{1157}(x, y) = \frac{y^{4} \left(2 - 2 \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}} + 1}\right)}{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}$$

$$T_{1157}(n, m, k) = \frac{2 k n {\binom{2 m + 4 n}{m}} {\binom{k + 2 n - 1}{n}}}{\left(k + n\right) \left(m + 2 n\right)}$$