$$U_{1089}(x, y) = \frac{\left(- 2 x - \sqrt{1 - 4 x} + 1\right)^{2} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{32 x^{4} y^{6}}$$

$$T_{1089}(n, m, k) = \frac{6 k^{2} {\binom{4 k + 2 n}{n}} {\binom{6 k + 2 m}{m}}}{\left(2 k + n\right) \left(3 k + m\right)}$$