$$U_{1199}(x, y) = \frac{64 y^{16} \left(- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{2 y^{4}} - \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}} + 1} + 1\right)^{2}}{x^{4} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{8}}$$

$$T_{1199}(n, m, k) = \frac{4 k n {\binom{4 k + 2 n}{n}} {\binom{2 m + 4 n}{m}}}{\left(2 k + n\right) \left(m + 2 n\right)}$$