$$U_{137}(x, y) = \frac{- 2 x + \sqrt{4 x + 4 y + 1} - 1}{- 2 x^{2} + 2 y}$$

$$T_{137}(n, m, k) = \frac{\left(-1\right)^{m + n} k {\binom{k + 2 m + n}{m}} {\binom{2 k + 2 m + 2 n}{n}}}{k + 2 m + n}$$