$$U_{343}(x, y) = \frac{y}{3} - \frac{- \frac{2 x}{3} - \frac{\left(y + 1\right)^{2}}{9}}{\sqrt[3]{\frac{x^{2}}{2 y + 2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + 4 \left(y + 1\right)^{2}\right)}}{18 y + 18} + \frac{x \left(y + 1\right)}{3} + \frac{\left(y + 1\right)^{3}}{27}}} + \sqrt[3]{\frac{x^{2}}{2 y + 2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + 4 \left(y + 1\right)^{2}\right)}}{18 y + 18} + \frac{x \left(y + 1\right)}{3} + \frac{\left(y + 1\right)^{3}}{27}} + \frac{1}{3}$$

$$T_{343}(n, m, k) = \begin{cases}{\binom{k}{m}}&\text{if n=0} ,\ \\\frac{2 k {\binom{k - 2 n}{m}} {\binom{2 k - 2 n - 1}{n - 1}}}{n} \end{cases} $$