Generating function
$$U_{1406}(x, y) = \left(x + 1\right)^{3} \left(y \left(x + 1\right)^{3} + 1\right)$$
Explicit formula
$$T_{1406}(n, m, k) = {\binom{k}{m}} {\binom{3 k + 3 m}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 3 | 6 | 0 | 0 | 0 | 0 | 0 |
| 3 | 15 | 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 0 | 0 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 | 0 | 0 | 0 |
| 0 | 6 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
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