$$U_{344}(x, y) = \frac{\frac{2 x}{3} + \frac{1}{9 \left(1 - y\right)^{2}}}{\sqrt[3]{\frac{x^{2} \left(1 - y\right)}{2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{2}}\right)} \left(1 - y\right)}{18} + \frac{x}{3 - 3 y} + \frac{1}{27 \left(1 - y\right)^{3}}}} + \sqrt[3]{\frac{x^{2} \left(1 - y\right)}{2} + \frac{\sqrt{3} x \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{2}}\right)} \left(1 - y\right)}{18} + \frac{x}{3 - 3 y} + \frac{1}{27 \left(1 - y\right)^{3}}} + \frac{1}{3 - 3 y}$$

$$T_{344}(n, m, k) = \begin{cases}{\binom{k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{2 k {\binom{2 k - 2 n - 1}{n - 1}} {\binom{k + m - 2 n - 1}{m}}}{n} \end{cases} $$