Generating function
$$U_{1160}(x, y) = \frac{\left(1 - \sqrt{- 4 x \left(y + 1\right)^{2} + 1}\right)^{2}}{4 x^{2} \left(y + 1\right)^{4}}$$
Explicit formula
$$T_{1160}(n, m, k) = \frac{2 k {\binom{2 n}{m}} {\binom{2 k + 2 n - 1}{n}}}{2 k + n}$$
Data table
1 0 0 0 0 0 0
2 4 2 0 0 0 0
5 2 3 2 5 0 0
14 84 21 28 21 84 14
42 336 1176 2352 294 2352 1176
132 132 594 1584 2772 33264 2772
429 5148 28314 9438 212355 339768 396396
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