Generating function
$$U_{1060}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right)^{2} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{16 x^{2} y^{4}}$$
Explicit formula
$$T_{1060}(n, m, k) = \frac{4 k^{2} {\binom{4 k + 2 m}{m}} {\binom{2 k + 2 n - 1}{n}}}{\left(2 k + m\right) \left(2 k + n\right)}$$
Data table
1 4 14 48 165 572 2002
2 8 28 96 33 1144 4004
5 2 7 24 825 286 1001
14 56 196 672 231 8008 28028
42 168 588 2016 693 24024 84084
132 528 1848 6336 2178 75504 264264
429 1716 6006 20592 70785 245388 858858
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