$$U_{553}(x, y) = \frac{1 - \sqrt{- 4 x \left(y + 1\right)^{4} + 1}}{2 x \left(y + 1\right)^{3}}$$

$$T_{553}(n, m, k) = \frac{k {\binom{k + 4 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$