Generating function
$$U_{320}(x, y) = \frac{1 - \sqrt{4 x y^{6} - 24 x y^{5} + 60 x y^{4} - 80 x y^{3} + 60 x y^{2} - 24 x y + 4 x + 1}}{2 y^{2} - 4 y + 2}$$
Explicit formula
$$T_{320}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{k - n - 1}{n - 1}} {\binom{2 k + m - 6 n - 1}{m}}}{n} \end{cases} $$
0 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 4 | -6 | 4 | -1 | 0 | 0 |
1 | -1 | 45 | -12 | 21 | -252 | 21 |
-2 | 32 | -24 | 112 | -364 | 8736 | -16016 |
5 | -11 | 1155 | -77 | 36575 | -13167 | 373065 |
-14 | 392 | -5292 | 45864 | -28665 | 137592 | -527436 |
42 | -1428 | 23562 | -251328 | 1947792 | -11686752 | 56485968 |
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