Generating function
$$U_{442}(x, y) = \frac{x^{2} - 2 x - 2 y + \left(x - 1\right) \sqrt{x^{2} - 2 x - 4 y + 1} + 1}{2 y^{2}}$$
Explicit formula
$$T_{442}(n, m, k) = \frac{k {\binom{2 k + 2 m}{m}} {\binom{2 k + 2 m + n - 1}{n}}}{k + m}$$
1 | 2 | 5 | 14 | 42 | 132 | 429 |
2 | 8 | 3 | 112 | 42 | 1584 | 6006 |
3 | 2 | 105 | 504 | 231 | 10296 | 45045 |
4 | 4 | 28 | 168 | 924 | 48048 | 24024 |
5 | 7 | 63 | 462 | 3003 | 18018 | 102102 |
6 | 112 | 126 | 11088 | 84084 | 576576 | 3675672 |
7 | 168 | 231 | 24024 | 21021 | 1633632 | 11639628 |
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