$$U_{381}(x, y) = \frac{y - \sqrt{4 x \left(y + 1\right) + \left(y + 1\right)^{2}} + 1}{2 x}$$

$$T_{381}(n, m, k) = \frac{\left(-1\right)^{k + m + n} k {\binom{k + 2 n - 1}{n}} {\binom{m + n - 1}{m}}}{k + n}$$