$$U_{556}(x, y) = \frac{\left(y + 1\right)^{2}}{2} + \frac{\sqrt{4 x \left(y + 1\right)^{6} + \left(y + 1\right)^{4}}}{2}$$

$$T_{556}(n, m, k) = \begin{cases}\frac{k {\binom{2 k + 2 n}{m}}}{k + n}&\text{if n==0 } ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{2 k + 2 n}{m}} {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$