Generating function
$$U_{1132}(x, y) = \frac{1}{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}} + 1}$$
Explicit formula
$$T_{1132}(n, m, k) = \frac{2 n {\binom{2 m + 4 n}{m}} {\binom{k + n - 1}{n}}}{m + 2 n}$$
Data table
nan 0 0 0 0 0 0
1 4 14 48 165 572 2002
1 8 44 208 91 3808 15504
1 12 9 544 2907 14364 67298
1 16 152 112 7084 4048 21528
1 2 23 2 14625 95004 56637
1 24 324 3248 2697 196416 1298528
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