$$U_{1139}(x, y) = \frac{1}{\left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{8 y^{3}} + 1\right)^{2}}$$

$$T_{1139}(n, m, k) = \frac{3 n {\binom{2 k + n - 1}{n}} {\binom{2 m + 3 n - 1}{m}}}{m + 3 n}$$