$$U_{1311}(x, y) = \frac{128 y^{18} \left(- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{4 y^{6}} - \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}} + 1} + 1\right)^{2}}{x^{4} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{9}}$$

$$T_{1311}(n, m, k) = \frac{6 k \left(k + n\right) {\binom{4 k + 2 n}{n}} {\binom{6 k + 2 m + 6 n}{m}}}{\left(2 k + n\right) \left(3 k + m + 3 n\right)}$$