Generating function
$$U_{729}(x, y) = x^{2} \left(y + 1\right)^{3} + 2 x \left(y + 1\right)^{2} + y + 1$$
Explicit formula
$$T_{729}(n, m, k) = {\binom{2 k}{n}} {\binom{k + n}{m}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 2 | 4 | 2 | 0 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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