Generating function
$$U_{1088}(x, y) = \frac{\left(- 2 x - \sqrt{1 - 4 x} + 1\right)^{2} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{16 x^{4} y^{4}}$$
Explicit formula
$$T_{1088}(n, m, k) = \frac{4 k^{2} {\binom{4 k + 2 m}{m}} {\binom{4 k + 2 n}{n}}}{\left(2 k + m\right) \left(2 k + n\right)}$$
Data table
1 4 14 48 165 572 2002
4 16 56 192 66 2288 8008
14 56 196 672 231 8008 28028
48 192 672 2304 792 27456 96096
165 66 231 792 27225 9438 33033
572 2288 8008 27456 9438 327184 1145144
2002 8008 28028 96096 33033 1145144 4008004
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