$$U_{778}(x, y) = - \frac{1}{x^{2} y^{3} - x^{2} + 2 x + y^{2} \left(- 3 x^{2} + 2 x\right) + y \left(3 x^{2} - 4 x + 1\right) - 1}$$

$$T_{778}(n, m, k) = {\binom{2 k + n - 1}{n}} {\binom{k + m - n - 1}{m}}$$