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
$$T_{1344}(n, m, k) = \frac{k {\binom{4 k + 4 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
Data table
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
Export
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