Generating function
$$U_{916}(x, y) = \frac{x}{3} + \frac{x^{2} + 2 x + 1}{9 \sqrt[3]{\frac{x^{3}}{27} + \frac{x^{2}}{9} + \frac{x \left(27 y + 3\right)}{27} + y + \frac{\sqrt{3} \sqrt{y \left(2 x^{2} + 4 x + 27 y + 2\right)} \left(x + 1\right)}{9} + \frac{1}{27}}} + \sqrt[3]{\frac{x^{3}}{27} + \frac{x^{2}}{9} + \frac{x \left(27 y + 3\right)}{27} + y + \frac{\sqrt{3} \sqrt{y \left(2 x^{2} + 4 x + 27 y + 2\right)} \left(x + 1\right)}{9} + \frac{1}{27}} + \frac{1}{3}$$
Explicit formula
$$T_{916}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0 } ,\ \\\frac{2^{m} k {\binom{k - 2 m}{n}} {\binom{k - 2 m - 1}{m - 1}}}{m} \end{cases} $$
1 | 2 | -8 | 56 | -48 | 4576 | -46592 |
1 | -2 | 24 | -28 | 336 | -41184 | 512512 |
0 | 2 | -48 | 84 | -1344 | 20592 | -3075072 |
0 | -2 | 8 | -196 | 4032 | -75504 | 13325312 |
0 | 2 | -12 | 392 | -1008 | 226512 | -46638592 |
0 | -2 | 168 | -7056 | 22176 | -5889312 | 139915776 |
0 | 2 | -224 | 1176 | -44352 | 13741728 | -373108736 |
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