$$U_{404}(x, y) = \frac{- y^{2} + \sqrt{x \sqrt{1 - 4 y} \left(2 - 4 y\right) + x \left(- 4 y^{2} + 8 y - 2\right) + y^{4}}}{x \sqrt{1 - 4 y} + x \left(2 y - 1\right)}$$

$$T_{404}(n, m, k) = \frac{k {\binom{k + 2 n}{n}} {\binom{2 k + 2 m + 4 n}{m}}}{k + m + 2 n}$$