Generating function
$$U_{292}(x, y) = y + \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Explicit formula
$$T_{292}(n, m, k) = \begin{cases}{\binom{k}{m}}&\text{if n=0} ,\ \\0&\text{if n>0 and 2*n+k-m=0 } ,\ \\\frac{\left(k - m\right) {\binom{k}{m}} {\binom{k - m + 3 n - 1}{n}}}{k - m + 2 n} \end{cases} $$
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
3 | 0 | 0 | 0 | 0 | 0 | 0 |
12 | 0 | 0 | 0 | 0 | 0 | 0 |
55 | 0 | 0 | 0 | 0 | 0 | 0 |
273 | 0 | 0 | 0 | 0 | 0 | 0 |
1428 | 0 | 0 | 0 | 0 | 0 | 0 |
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