$$U_{867}(x, y) = \left(1 - y\right)^{3} \left(x + \frac{1}{\left(1 - y\right)^{5}}\right)$$

$$T_{867}(n, m, k) = {\binom{k}{n}} {\binom{2 k + m - 5 n - 1}{m}}$$