Generating function
$$U_{890}(x, y) = \frac{2 x + \sqrt{4 x + \left(y + 1\right)^{4}} \left(y + 1\right)^{2} + \left(y + 1\right)^{4}}{2 y + 2}$$
Explicit formula
$$T_{890}(n, m, k) = \begin{cases}{\binom{3 k}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{3 k - 4 n}{m}} {\binom{- 2 k + 2 n - 1}{n - 1}}}{n} \end{cases} $$
1 | 3 | 3 | 1 | 0 | 0 | 0 |
2 | -2 | 2 | -2 | 2 | -2 | 2 |
-1 | 5 | -15 | 35 | -7 | 126 | -21 |
2 | -18 | 9 | -33 | 99 | -2574 | 6006 |
-5 | 65 | -455 | 2275 | -91 | 3094 | -9282 |
14 | -238 | 2142 | -13566 | 6783 | -284886 | 1044582 |
-42 | 882 | -9702 | 74382 | -446292 | 223146 | -966966 |
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