Generating function
$$U_{368}(x, y) = \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{3}}\right)}}{18} + \frac{1}{27 \left(1 - y\right)^{3}}} + \frac{1}{3 - 3 y} + \frac{1}{9 \left(1 - y\right)^{2} \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - y\right)^{3}}\right)}}{18} + \frac{1}{27 \left(1 - y\right)^{3}}}}$$
Explicit formula
$$T_{368}(n, m, k) = \begin{cases}1&\text{if n=0} ,\ \\\frac{k {\binom{k - 2 n - 1}{n - 1}} {\binom{k + m - 3 n - 1}{m}}}{n},\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + n - 1}{m - 1}}}{m}&\text{if n=0} \end{cases} $$
1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | -2 | 1 | 0 | 0 | 0 | 0 |
-2 | 1 | -2 | 2 | -1 | 2 | 0 |
7 | -56 | 196 | -392 | 49 | -392 | 196 |
-3 | 33 | -165 | 495 | -99 | 1386 | -1386 |
143 | -2002 | 13013 | -52052 | 143143 | -286286 | 429429 |
-728 | 12376 | -99008 | 49504 | -173264 | 4504864 | -9009728 |
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