$$U_{405}(x, y) = \frac{\sqrt{\frac{2 x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{y^{2}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}}}}{2} + \frac{- 2 y - \sqrt{1 - 4 y} + 1}{4 y^{2}}$$

$$T_{405}(n, m, k) = \begin{cases}\frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if n>0 } ,\ \\1&\text{if m=0 and n = 0} ,\ \\\frac{2 k {\binom{k - n}{n}} {\binom{2 k + 2 m - 2 n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$