$$U_{1176}(x, y) = \frac{64 y^{9} \left(1 - \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}} + 1}\right)^{3}}{x^{3} \left(1 - \sqrt{1 - 4 y}\right)^{9}}$$

$$T_{1176}(n, m, k) = \frac{9 k n {\binom{3 k + 2 n - 1}{n}} {\binom{2 m + 3 n - 1}{m}}}{\left(3 k + n\right) \left(m + 3 n\right)}$$