$$U_{1046}(x, y) = \frac{1 - \sqrt{1 - 4 y}}{2 y \left(1 - x\right)^{3}}$$

$$T_{1046}(n, m, k) = \frac{k {\binom{k + 2 m - 1}{m}} {\binom{3 k + n - 1}{n}}}{k + m}$$