Generating function
$$U_{1281}(x, y) = \frac{\left(1 - \sqrt{- 4 x \left(y + 1\right)^{3} + 1}\right)^{3}}{8 x^{3} \left(y + 1\right)^{6}}$$
Explicit formula
$$T_{1281}(n, m, k) = \frac{3 k {\binom{3 k + 3 n}{m}} {\binom{3 k + 2 n - 1}{n}}}{3 k + n}$$
1 | 3 | 3 | 1 | 0 | 0 | 0 |
3 | 18 | 45 | 6 | 45 | 18 | 3 |
9 | 81 | 324 | 756 | 1134 | 1134 | 756 |
28 | 336 | 1848 | 616 | 1386 | 22176 | 25872 |
9 | 135 | 945 | 4095 | 12285 | 27027 | 45045 |
297 | 5346 | 45441 | 242352 | 90882 | 2544696 | 5513508 |
1001 | 21021 | 21021 | 133133 | 5990985 | 20369349 | 54318264 |
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