$$U_{1207}(x, y) = \frac{8 y^{6} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{y} - \sqrt{- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1} + 1\right)^{3}}{x^{6} \left(1 - \sqrt{1 - 4 y}\right)^{6}}$$

$$T_{1207}(n, m, k) = \frac{3 k n {\binom{6 k + 2 n}{n}} {\binom{2 m + n - 1}{m}}}{\left(3 k + n\right) \left(m + n\right)}$$