Generating function
$$U_{210}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{3} - 12 x^{2} - 12 x - 4\right) + 1}}{y \left(2 x + 2\right)}$$
Explicit formula
$$T_{210}(n, m, k) = \frac{k {\binom{2 k + 3 m}{n}} {\binom{k + 2 m - 1}{m}}}{k + m}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
2 | 5 | 16 | 55 | 196 | 714 | 264 |
1 | 1 | 56 | 275 | 1274 | 5712 | 2508 |
0 | 1 | 112 | 825 | 5096 | 2856 | 15048 |
0 | 5 | 14 | 165 | 14014 | 9996 | 63954 |
0 | 1 | 112 | 231 | 28028 | 259896 | 2046528 |
0 | 0 | 56 | 231 | 42042 | 519792 | 511632 |
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