$$U_{1032}(x, y) = \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4} \left(4 - 4 x\right)}$$

$$T_{1032}(n, m, k) = \frac{2 k {\binom{4 k + 2 m}{m}} {\binom{k + n - 1}{n}}}{2 k + m}$$