Generating function
$$U_{1153}(x, y) = \frac{1}{\left(- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}} + 1\right)^{3}}$$
Explicit formula
$$T_{1153}(n, m, k) = \frac{2 n {\binom{2 m + 4 n}{m}} {\binom{3 k + n - 1}{n}}}{m + 2 n}$$
Data table
nan 0 0 0 0 0 0
3 12 42 144 495 1716 6006
6 48 264 1248 546 22848 93024
1 12 9 544 2907 14364 67298
15 24 228 168 10626 6072 32292
21 42 483 42 307125 1995084 1189377
28 672 9072 90944 75516 5499648 36358784
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