Generating function
$$U_{552}(x, y) = \frac{- y - 1}{x \left(y + 1\right)^{3} - 1}$$
Explicit formula
$$T_{552}(n, m, k) = {\binom{k + 3 n}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 4 | 6 | 4 | 1 | 0 | 0 |
| 1 | 7 | 21 | 35 | 35 | 21 | 7 |
| 1 | 1 | 45 | 12 | 21 | 252 | 21 |
| 1 | 13 | 78 | 286 | 715 | 1287 | 1716 |
| 1 | 16 | 12 | 56 | 182 | 4368 | 8008 |
| 1 | 19 | 171 | 969 | 3876 | 11628 | 27132 |
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