Generating function
$$U_{363}(x, y) = \frac{y^{2}}{2} + y - \frac{\sqrt{4 x + y^{4} + 4 y^{3} + 6 y^{2} + 4 y + 1}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{363}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{2 k - 4 n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$
0 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 2 | -3 | 4 | -5 | 6 | -7 |
1 | -6 | 21 | -56 | 126 | -252 | 462 |
-2 | 2 | -11 | 44 | -143 | 4004 | -1001 |
5 | -7 | 525 | -28 | 119 | -4284 | 13566 |
-14 | 252 | -2394 | 1596 | -8379 | 368676 | -1413258 |
42 | -924 | 10626 | -85008 | 5313 | -276276 | 1243242 |
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