$$U_{1057}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right) \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{16 x y^{6}}$$

$$T_{1057}(n, m, k) = \frac{3 k^{2} {\binom{6 k + 2 m}{m}} {\binom{k + 2 n - 1}{n}}}{\left(k + n\right) \left(3 k + m\right)}$$