Generating function
$$U_{390}(x, y) = \frac{\left(y + 1\right)^{2}}{2} + \frac{\sqrt{4 x \left(y + 1\right)^{2} + \left(y + 1\right)^{4}}}{2}$$
Explicit formula
$$T_{390}(n, m, k) = \begin{cases}{\binom{2 k}{m}}&\text{if n=0} ,\ \\\frac{k {\binom{2 k - 2 n}{m}} {\binom{k - n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 2 | -3 | 4 | -5 | 6 | -7 |
2 | -8 | 2 | -4 | 7 | -112 | 168 |
-5 | 3 | -105 | 28 | -63 | 126 | -231 |
14 | -112 | 504 | -168 | 462 | -11088 | 24024 |
-42 | 42 | -231 | 924 | -3003 | 84084 | -21021 |
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