Generating function
$$U_{1410}(x, y) = \left(y + 1\right)^{2} \left(x \left(y + 1\right)^{3} + 1\right)$$
Explicit formula
$$T_{1410}(n, m, k) = {\binom{k}{n}} {\binom{2 k + 3 n}{m}}$$
| 1 | 2 | 1 | 0 | 0 | 0 | 0 |
| 1 | 5 | 1 | 1 | 5 | 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 | 0 | 0 | 0 | 0 | 0 |
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