Generating function
$$U_{1133}(x, y) = \frac{1}{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{8 y^{6}} + 1}$$
Explicit formula
$$T_{1133}(n, m, k) = \frac{3 n {\binom{2 m + 6 n}{m}} {\binom{k + n - 1}{n}}}{m + 3 n}$$
| nan | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 6 | 27 | 11 | 429 | 1638 | 6188 |
| 1 | 12 | 9 | 544 | 2907 | 14364 | 67298 |
| 1 | 18 | 189 | 1518 | 1035 | 6318 | 356265 |
| 1 | 24 | 324 | 3248 | 2697 | 196416 | 1298528 |
| 1 | 3 | 495 | 595 | 58275 | 493506 | 374699 |
| 1 | 36 | 702 | 984 | 111069 | 1072764 | 9203634 |
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