$$U_{1056}(x, y) = 15661$$ $$U_{1056}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right) \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{8 x y^{4}}$$

$$T_{1056}(n, m, k) = \begin{cases}\frac{2 k^{2} {\binom{4 k + 2 m}{m}} {\binom{k + 2 n - 1}{n}}}{\left(k + n\right) \left(2 k + m\right)},\ \\1&\text{if n=0,m=0} \end{cases} $$