$$U_{1277}(x, y) = \frac{y^{4} \left(1 - \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}} + 1}\right)^{2}}{x^{2} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}$$

$$T_{1277}(n, m, k) = \frac{4 k \left(k + n\right) {\binom{2 k + 2 n - 1}{n}} {\binom{4 k + 2 m + 4 n}{m}}}{\left(2 k + n\right) \left(2 k + m + 2 n\right)}$$