Generating function
$$U_{447}(x, y) = \frac{1}{\left(1 - x\right)^{2} \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{447}(n, m, k) = {\binom{2 k + n - 1}{n}} {\binom{3 k + m - 1}{m}}$$
| 1 | 3 | 6 | 1 | 15 | 21 | 28 |
| 2 | 6 | 12 | 2 | 3 | 42 | 56 |
| 3 | 9 | 18 | 3 | 45 | 63 | 84 |
| 4 | 12 | 24 | 4 | 6 | 84 | 112 |
| 5 | 15 | 3 | 5 | 75 | 105 | 14 |
| 6 | 18 | 36 | 6 | 9 | 126 | 168 |
| 7 | 21 | 42 | 7 | 105 | 147 | 196 |
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