$$U_{1024}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2} \left(x + 1\right)^{3}}{4 y^{2}}$$

$$T_{1024}(n, m, k) = \frac{2 k {\binom{3 k}{n}} {\binom{2 k + 2 m - 1}{m}}}{2 k + m}$$