$$U_{1062}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right)^{3} \left(y + 1\right)}{8 x^{3}}$$

$$T_{1062}(n, m, k) = \frac{3 k {\binom{k}{m}} {\binom{3 k + 2 n - 1}{n}}}{3 k + n}$$