Generating function
$$U_{1344}(x, y) = \frac{1 - \sqrt{- 4 x y^{4} - 16 x y^{3} - 24 x y^{2} - 16 x y - 4 x + 1}}{2 x}$$
Explicit formula
$$T_{1344}(n, m, k) = \frac{k {\binom{4 k + 4 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
1 | 4 | 6 | 4 | 1 | 0 | 0 |
1 | 8 | 28 | 56 | 7 | 56 | 28 |
2 | 24 | 132 | 44 | 99 | 1584 | 1848 |
5 | 8 | 6 | 28 | 91 | 2184 | 4004 |
14 | 28 | 266 | 1596 | 6783 | 217056 | 54264 |
42 | 1008 | 11592 | 85008 | 446292 | 1785168 | 5653032 |
132 | 3696 | 49896 | 432432 | 27027 | 1297296 | 4972968 |
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