$$U_{172}(x, y) = \frac{- x^{2} + 2 x + \sqrt{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + y \left(4 x - 4\right) + 1} - 1}{y \left(2 x - 2\right)}$$

$$T_{172}(n, m, k) = \begin{cases}1&\text{if m=0 and n=0} ,\ \\\frac{k {\binom{k + 2 m - 1}{m}} {\binom{2 k + 3 m + n - 1}{n}}}{k + m} \end{cases} $$