Generating function
$$U_{738}(x, y) = \frac{\left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right)^{2}}{\left(1 - y\right)^{2}}$$
Explicit formula
$$T_{738}(n, m, k) = \begin{cases}{\binom{2 k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 3 n - 1}{n - 1}} {\binom{2 k + m - 1}{m}}}{n}&\text{if n>0} \end{cases} $$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 4 | 6 | 8 | 1 | 12 | 14 |
-3 | -6 | -9 | -12 | -15 | -18 | -21 |
1 | 2 | 3 | 4 | 5 | 6 | 7 |
-42 | -84 | -126 | -168 | -21 | -252 | -294 |
198 | 396 | 594 | 792 | 99 | 1188 | 1386 |
-1001 | -2002 | -3003 | -4004 | -5005 | -6006 | -7007 |
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