$$U_{1171}(x, y) = \frac{\left(1 - y\right)^{3} \left(1 - \sqrt{- \frac{4 x}{1 - y} + 1}\right)^{3}}{8 x^{3}}$$

$$T_{1171}(n, m, k) = \frac{3 k {\binom{3 k + 2 n - 1}{n}} {\binom{m + n - 1}{m}}}{3 k + n}$$