$$U_{345}(x, y) = \frac{\frac{2 x}{3} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{36 y^{2}}}{\sqrt[3]{\frac{x^{2} y}{1 - \sqrt{1 - 4 y}} + \frac{\sqrt{3} x y \sqrt{x \left(27 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}}\right)}}{9 - 9 \sqrt{1 - 4 y}} + \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{6 y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{216 y^{3}}}} + \sqrt[3]{\frac{x^{2} y}{1 - \sqrt{1 - 4 y}} + \frac{\sqrt{3} x y \sqrt{x \left(27 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}}\right)}}{9 - 9 \sqrt{1 - 4 y}} + \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{6 y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{216 y^{3}}} + \frac{1 - \sqrt{1 - 4 y}}{6 y}$$

$$T_{345}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 m - 1}{m}}}{k + m}&\text{if n=0} ,\ \\\frac{2 {\binom{2 k - 2 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\\frac{2 \left(-1\right)^{m - 1} k \left(k - 2 n\right) {\binom{2 k - 2 n - 1}{n - 1}} {\binom{- k - m + 2 n - 1}{m - 1}}}{m n}&\text{if m>0,n>0} \end{cases} $$