$$U_{1307}(x, y) = \frac{16 y^{6} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{2 y^{2}} - \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}} + 1} + 1\right)^{2}}{x^{4} \left(1 - \sqrt{1 - 4 y}\right)^{6}}$$

$$T_{1307}(n, m, k) = \frac{4 k \left(k + n\right) {\binom{4 k + 2 n}{n}} {\binom{2 k + 2 m + 2 n - 1}{m}}}{\left(2 k + n\right) \left(2 k + m + 2 n\right)}$$