$$U_{1191}(x, y) = \frac{\left(- 2 x \left(y + 1\right)^{3} - \sqrt{- 4 x \left(y + 1\right)^{3} + 1} + 1\right)^{2}}{4 x^{4} \left(y + 1\right)^{12}}$$

$$T_{1191}(n, m, k) = \frac{2 k {\binom{3 n}{m}} {\binom{4 k + 2 n}{n}}}{2 k + n}$$