$$U_{1069}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right)^{3} \left(1 - \sqrt{1 - 4 y}\right)^{2}}{32 x^{3} y^{2}}$$

$$T_{1069}(n, m, k) = \frac{6 k^{2} {\binom{2 k + 2 m - 1}{m}} {\binom{3 k + 2 n - 1}{n}}}{\left(2 k + m\right) \left(3 k + n\right)}$$