$$U_{1189}(x, y) = \frac{\left(- 2 x \left(y + 1\right) - \sqrt{- 4 x \left(y + 1\right) + 1} + 1\right)^{2}}{4 x^{4} \left(y + 1\right)^{4}}$$

$$T_{1189}(n, m, k) = \frac{2 k {\binom{n}{m}} {\binom{4 k + 2 n}{n}}}{2 k + n}$$