$$U_{382}(x, y) = \frac{y}{3} + \frac{\left(y + 1\right)^{2}}{9 \sqrt[3]{\frac{x \left(y + 1\right)}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + 4 \left(y + 1\right)^{2}\right)} \left(y + 1\right)}{18} + \frac{\left(y + 1\right)^{3}}{27}}} + \sqrt[3]{\frac{x \left(y + 1\right)}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + 4 \left(y + 1\right)^{2}\right)} \left(y + 1\right)}{18} + \frac{\left(y + 1\right)^{3}}{27}} + \frac{1}{3}$$

$$T_{382}(n, m, k) = \begin{cases}1&\text{if m=0, n = 0} ,\ \\\frac{k {\binom{k - 2 n}{m}} {\binom{k - 2 n - 1}{n - 1}}}{n}&\text{if n>0} ,\ \\\frac{k {\binom{k - n - 1}{m - 1}}}{m}&\text{if n=0} \end{cases} $$