$$U_{531}(x, y) = \left(1 - y\right)^{4} \left(x + \frac{1}{\left(1 - y\right)^{6}}\right)$$

$$T_{531}(n, m, k) = {\binom{k}{n}} {\binom{2 k + m - 6 n - 1}{m}}$$