Generating function
$$U_{1150}(x, y) = \frac{1}{\left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}} + 1\right)^{3}}$$
Explicit formula
$$T_{1150}(n, m, k) = \frac{2 n {\binom{3 k + n - 1}{n}} {\binom{2 m + 2 n - 1}{m}}}{m + 2 n}$$
Data table
nan 0 0 0 0 0 0
3 6 15 42 126 396 1287
6 24 84 288 99 3432 12012
1 6 27 11 429 1638 6188
15 12 66 312 1365 5712 23256
21 21 1365 735 357 162792 712215
28 336 252 15232 81396 402192 1884344
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