$$U_{1200}(x, y) = \frac{1024 y^{24} \left(- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{4 y^{6}} - \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}} + 1} + 1\right)^{2}}{x^{4} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{12}}$$

$$T_{1200}(n, m, k) = \frac{6 k n {\binom{4 k + 2 n}{n}} {\binom{2 m + 6 n}{m}}}{\left(2 k + n\right) \left(m + 3 n\right)}$$