Generating function
$$U_{1154}(x, y) = \frac{1}{\left(- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{8 y^{6}} + 1\right)^{3}}$$
Explicit formula
$$T_{1154}(n, m, k) = \frac{3 n {\binom{2 m + 6 n}{m}} {\binom{3 k + n - 1}{n}}}{m + 3 n}$$
Data table
nan 0 0 0 0 0 0
3 18 81 33 1287 4914 18564
6 72 54 3264 17442 86184 403788
1 18 189 1518 1035 6318 356265
15 36 486 4872 40455 294624 1947792
21 63 10395 12495 1223775 10363626 7868679
28 1008 19656 27552 3109932 30037392 257701752
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