$$U_{277}(x, y) = x + y^{3} + y$$

$$T_{277}(n, m, k) = \frac{\left(\left(-1\right)^{- k + m + n} + 1\right) {\binom{k}{n}} {\binom{k - n}{- \frac{k}{2} + \frac{m}{2} + \frac{n}{2}}}}{2}$$