$$U_{401}(x, y) = \sqrt[3]{\frac{x \left(1 - \sqrt{1 - 4 y}\right)}{4 y} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}}\right)} \left(1 - \sqrt{1 - 4 y}\right)}{36 y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{216 y^{3}}} + \frac{1 - \sqrt{1 - 4 y}}{6 y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{36 y^{2} \sqrt[3]{\frac{x \left(1 - \sqrt{1 - 4 y}\right)}{4 y} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2}}\right)} \left(1 - \sqrt{1 - 4 y}\right)}{36 y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3}}{216 y^{3}}}}$$

$$T_{401}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 3 n - 1}{n - 1}}}{n}&\text{if n>0 and m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{k - 2 n}{n}} {\binom{- k - m + 2 n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$