$$U_{1211}(x, y) = \frac{512 y^{24} \left(- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{2 y^{4}} - \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}} + 1} + 1\right)^{3}}{x^{6} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{12}}$$

$$T_{1211}(n, m, k) = \frac{6 k n {\binom{6 k + 2 n}{n}} {\binom{2 m + 4 n}{m}}}{\left(3 k + n\right) \left(m + 2 n\right)}$$