$$U_{967}(x, y) = \frac{- x - \sqrt{- 4 x^{2} y + x^{2} - 2 x + 1} + 1}{2 x^{2} y}$$

$$T_{967}(n, m, k) = \frac{k {\binom{k + n}{- m + n}} {\binom{- m + n}{m}}}{k + n}$$