$$U_{420}(x, y) = \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{6}}\right)}}{18} + \frac{1}{27 \left(1 - y\right)^{6}}} + \frac{1}{3 \left(1 - y\right)^{2}} + \frac{1}{9 \left(1 - y\right)^{4} \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{6}}\right)}}{18} + \frac{1}{27 \left(1 - y\right)^{6}}}}$$

$$T_{420}(n, m, k) = \begin{cases}1&\text{if m=0 and n=0} ,\ \\\frac{2 \left(-1\right)^{m - 1} k {\binom{- 2 k + 2 n - 1}{m - 1}}}{m}&\text{if m>0} ,\ \\\frac{k {\binom{k - 2 n - 1}{n - 1}} {\binom{2 k + m - 6 n - 1}{m}}}{n}&\text{if n>0} \end{cases} $$