Generating function
$$U_{301}(x, y) = \frac{2 \sin{\left(\frac{\arcsin{\left(\sqrt{\frac{27 x}{4} + \frac{27 y}{4}} \right)}}{3} \right)}}{\sqrt{3 x + 3 y}}$$
Explicit formula
$$T_{301}(n, m, k) = \frac{k {\binom{m + n}{m}} {\binom{k + 3 m + 3 n - 1}{m + n}}}{k + 2 m + 2 n}$$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | 6 | 36 | 22 | 1365 | 8568 | 54264 |
3 | 36 | 33 | 273 | 2142 | 162792 | 1211364 |
12 | 22 | 273 | 2856 | 27132 | 2422728 | 207207 |
55 | 1365 | 2142 | 27132 | 302841 | 3108105 | 30045015 |
273 | 8568 | 162792 | 2422728 | 3108105 | 36054018 | 388756368 |
1428 | 54264 | 1211364 | 207207 | 30045015 | 388756368 | 46262007792 |
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