Generating function
$$U_{1190}(x, y) = \frac{\left(- 2 x \left(y + 1\right)^{2} - \sqrt{- 4 x \left(y + 1\right)^{2} + 1} + 1\right)^{2}}{4 x^{4} \left(y + 1\right)^{8}}$$
Explicit formula
$$T_{1190}(n, m, k) = \frac{2 k {\binom{2 n}{m}} {\binom{4 k + 2 n}{n}}}{2 k + n}$$
Data table
1 0 0 0 0 0 0
4 8 4 0 0 0 0
14 56 84 56 14 0 0
48 288 72 96 72 288 48
165 132 462 924 1155 924 462
572 572 2574 6864 12012 144144 12012
2002 24024 132132 44044 99099 1585584 1849848
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