$$U_{324}(x, y) = \frac{1}{2} - \frac{\sqrt{4 x y^{3} + 12 x y^{2} + 12 x y + 4 x + 1}}{2}$$

$$T_{324}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\\frac{\left(-1\right)^{n} k {\binom{3 n}{m}} {\binom{- k + 2 n - 1}{n - 1}}}{n} \end{cases} $$