$$U_{1097}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2} \left(- 2 x - \sqrt{1 - 4 x} + 1\right)^{3}}{32 x^{6} y^{2}}$$

$$T_{1097}(n, m, k) = \frac{6 k^{2} {\binom{6 k + 2 n}{n}} {\binom{2 k + 2 m - 1}{m}}}{\left(2 k + m\right) \left(3 k + n\right)}$$