$$U_{348}(x, y) = \frac{\frac{2 x}{3} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{36 y^{4}}}{\sqrt[3]{\frac{x^{2} y^{2}}{- 2 y - \sqrt{1 - 4 y} + 1} + \frac{\sqrt{3} x y^{2} \sqrt{x \left(27 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}}\right)}}{- 18 y - 9 \sqrt{1 - 4 y} + 9} + \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{6 y^{2}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{216 y^{6}}}} + \sqrt[3]{\frac{x^{2} y^{2}}{- 2 y - \sqrt{1 - 4 y} + 1} + \frac{\sqrt{3} x y^{2} \sqrt{x \left(27 x + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{y^{4}}\right)}}{- 18 y - 9 \sqrt{1 - 4 y} + 9} + \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{6 y^{2}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{216 y^{6}}} + \frac{- 2 y - \sqrt{1 - 4 y} + 1}{6 y^{2}}$$

$$T_{348}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{k {\binom{2 k + 2 m}{m}}}{k + m}&\text{if n=0} ,\ \\\frac{2 k {\binom{2 k - 2 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\\frac{4 k \left(k - 2 n\right) {\binom{2 k - 2 n - 1}{n - 1}} {\binom{2 k + 2 m - 4 n - 1}{m - 1}}}{m n}&\text{if n>0 and m>0} \end{cases} $$