$$U_{1129}(x, y) = \left(\frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{8 y^{6}} + 1\right)^{3}$$

$$T_{1129}(n, m, k) = \frac{3 n {\binom{3 k}{n}} {\binom{2 m + 6 n}{m}}}{m + 3 n}$$