Generating function
$$U_{385}(x, y) = \sqrt[3]{\frac{x}{2 - 2 y} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{2}}\right)}}{18 - 18 y} + \frac{1}{27 \left(1 - y\right)^{3}}} + \frac{1}{3 - 3 y} + \frac{1}{9 \left(1 - y\right)^{2} \sqrt[3]{\frac{x}{2 - 2 y} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{2}}\right)}}{18 - 18 y} + \frac{1}{27 \left(1 - y\right)^{3}}}}$$
Explicit formula
$$T_{385}(n, m, k) = \begin{cases}1&\text{if m=0,n=0} ,\ \\\frac{k {\binom{k - 2 n - 1}{n - 1}} {\binom{k + m - 2 n - 1}{m}}}{n}&\text{if n>0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + n - 1}{m - 1}}}{m}&\text{if n=0} \end{cases} $$
1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | -1 | 0 | 0 | 0 | 0 | 0 |
-2 | 6 | -6 | 2 | 0 | 0 | 0 |
7 | -35 | 7 | -7 | 35 | -7 | 0 |
-3 | 21 | -63 | 105 | -105 | 63 | -21 |
143 | -1287 | 5148 | -12012 | 18018 | -18018 | 12012 |
-728 | 8008 | -4004 | 12012 | -24024 | 336336 | -336336 |
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