Generating function
$$U_{1128}(x, y) = \left(\frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}} + 1\right)^{3}$$
Explicit formula
$$T_{1128}(n, m, k) = \frac{2 n {\binom{3 k}{n}} {\binom{2 m + 4 n}{m}}}{m + 2 n}$$
Data table
nan 0 0 0 0 0 0
3 12 42 144 495 1716 6006
3 24 132 624 273 11424 46512
1 12 9 544 2907 14364 67298
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
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