$$U_{1249}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}} + 1\right)^{2}}$$

$$T_{1249}(n, m, k) = \frac{\left(2 k + 2 n\right) {\binom{2 k + n - 1}{n}} {\binom{2 k + 2 m + 2 n - 1}{m}}}{2 k + m + 2 n}$$