$$U_{1235}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right) \left(\frac{x \left(1 - \sqrt{1 - 4 y}\right)}{2 y} + 1\right)^{3}}{2 y}$$

$$T_{1235}(n, m, k) = \frac{\left(k + n\right) {\binom{3 k}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$