$$U_{1278}(x, y) = \frac{2 y^{6} \left(1 - \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}} + 1}\right)^{2}}{x^{2} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}$$

$$T_{1278}(n, m, k) = \frac{6 k \left(k + n\right) {\binom{2 k + 2 n - 1}{n}} {\binom{6 k + 2 m + 6 n}{m}}}{\left(2 k + n\right) \left(3 k + m + 3 n\right)}$$