$$U_{188}(x, y) = \frac{\sqrt{4 x + 4 y + 1} - 1}{2 x + 2 y}$$

$$T_{188}(n, m, k) = \frac{\left(-1\right)^{- m + n} k {\binom{k + m + 2 n - 1}{n}} {\binom{k + 2 m + 2 n - 1}{m}}}{k + m + n}$$