$$U_{1269}(x, y) = \frac{1 - \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}} + 1}}{2 x}$$

$$T_{1269}(n, m, k) = \frac{3 k {\binom{k + 2 n - 1}{n}} {\binom{6 k + 2 m + 6 n}{m}}}{3 k + m + 3 n}$$