$$U_{1208}(x, y) = \frac{512 y^{12} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{2 y^{2}} - \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}} + 1} + 1\right)^{3}}{x^{6} \left(1 - \sqrt{1 - 4 y}\right)^{12}}$$

$$T_{1208}(n, m, k) = \frac{6 k n {\binom{6 k + 2 n}{n}} {\binom{2 m + 2 n - 1}{m}}}{\left(3 k + n\right) \left(m + 2 n\right)}$$