Generating function
$$U_{1134}(x, y) = \frac{1}{\left(- x \left(y + 1\right)^{2} + 1\right)^{2}}$$
Explicit formula
$$T_{1134}(n, m, k) = {\binom{2 n}{m}} {\binom{2 k + n - 1}{n}}$$
Data table
1 0 0 0 0 0 0
2 4 2 0 0 0 0
3 12 18 12 3 0 0
4 24 6 8 6 24 4
5 4 14 28 35 28 14
6 6 27 72 126 1512 126
7 84 462 154 3465 5544 6468
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