Generating function
$$U_{392}(x, y) = \frac{\left(y + 1\right)^{4}}{9 \sqrt[3]{\frac{x \left(y + 1\right)^{2}}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + 4 \left(y + 1\right)^{4}\right)} \left(y + 1\right)^{2}}{18} + \frac{\left(y + 1\right)^{6}}{27}}} + \frac{\left(y + 1\right)^{2}}{3} + \sqrt[3]{\frac{x \left(y + 1\right)^{2}}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + 4 \left(y + 1\right)^{4}\right)} \left(y + 1\right)^{2}}{18} + \frac{\left(y + 1\right)^{6}}{27}}$$
Explicit formula
$$T_{392}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{2 k {\binom{2 k - 2 n - 1}{m - 1}}}{m}&\text{if m>0} ,\ \\\frac{k {\binom{2 k - 4 n}{m}} {\binom{k - 2 n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
1 | 2 | -1 | 2/3 | -1/2 | 2/5 | -1/3 |
-2 | 2 | -3 | 4 | -5 | 6 | -7 |
7 | 2 | -5 | 1 | -35/2 | 28 | -42 |
-3 | 2 | -7 | 56/3 | -42 | 84 | -154 |
143 | 2 | -9 | 3 | -165/2 | 198 | -429 |
-728 | 2 | -11 | 44 | -143 | 2002/5 | -1001 |
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