$$U_{1319}(x, y) = \frac{64 y^{10} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{2 y^{2}} - \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}} + 1} + 1\right)^{3}}{5 x^{6} \left(1 - \sqrt{1 - 4 y}\right)}$$

$$T_{1319}(n, m, k) = \frac{6 k \left(k + n\right) {\binom{6 k + 2 n}{n}} {\binom{2 k + 2 m + 2 n - 1}{m}}}{\left(3 k + n\right) \left(2 k + m + 2 n\right)}$$