Generating function
$$U_{1287}(x, y) = \frac{8 y^{6} \left(1 - \sqrt{- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}} + 1}\right)^{3}}{x^{3} \left(1 - \sqrt{1 - 4 y}\right)^{6}}$$
Explicit formula
$$T_{1287}(n, m, k) = \frac{9 k \left(k + n\right) {\binom{3 k + 2 n - 1}{n}} {\binom{3 k + 2 m + 3 n - 1}{m}}}{\left(3 k + n\right) \left(3 k + m + 3 n\right)}$$
| 1 | 3 | 9 | 28 | 9 | 297 | 1001 |
| 3 | 18 | 81 | 33 | 1287 | 4914 | 18564 |
| 9 | 81 | 486 | 2457 | 1134 | 49572 | 209304 |
| 28 | 336 | 252 | 15232 | 81396 | 402192 | 1884344 |
| 9 | 135 | 1215 | 855 | 51975 | 286902 | 148005 |
| 297 | 5346 | 56133 | 450846 | 307395 | 1876446 | 105810705 |
| 1001 | 21021 | 252252 | 2277275 | 17216199 | 115216101 | 705520816 |
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