Generating function
$$U_{460}(x, y) = \frac{\left(y + 1\right)^{4} + \sqrt{4 x \left(y + 1\right)^{2} + \left(y + 1\right)^{8}}}{2 \left(y + 1\right)^{2}}$$
Explicit formula
$$T_{460}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\{\binom{2 k}{m}}&\text{if m>0 and n=0} ,\ \\\frac{k {\binom{2 k - 6 n}{m}} {\binom{k - n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
1 | -4 | 1 | -2 | 35 | -56 | 84 |
-1 | 1 | -55 | 22 | -715 | 2002 | -5005 |
2 | -32 | 272 | -1632 | 7752 | -31008 | 108528 |
-5 | 11 | -1265 | 1012 | -6325 | 3289 | -148005 |
14 | -392 | 5684 | -5684 | 44051 | -2819264 | 15505952 |
-42 | 1428 | -2499 | 29988 | -277389 | 21081564 | -137030166 |
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