$$U_{1317}(x, y) = \frac{\left(1 - y\right)^{15} \left(- \frac{2 x}{\left(1 - y\right)^{3}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{3}} + 1} + 1\right)^{3}}{8 x^{6}}$$

$$T_{1317}(n, m, k) = \frac{3 k {\binom{6 k + 2 n}{n}} {\binom{3 k + m + 3 n - 1}{m}}}{3 k + n}$$