Generating function
$$U_{449}(x, y) = x - \frac{\sqrt{\frac{4 x}{\left(1 - y\right)^{3}} + \frac{1}{\left(1 - y\right)^{6}}}}{2} + \frac{1}{2 \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{449}(n, m, k) = \begin{cases}0&\text{if n<2*k} ,\ \\- \frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\- \frac{3 \left(-1\right)^{m - 1} k {\binom{- 3 k + 3 n - 1}{m - 1}} {\binom{2 k - n - 1}{n}}}{m} \end{cases} $$
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | -3 | 3 | -1 | 0 | 0 | 0 |
-2 | 12 | -3 | 4 | -3 | 12 | -2 |
5 | -45 | 18 | -42 | 63 | -63 | 42 |
-14 | 168 | -924 | 308 | -693 | 11088 | -12936 |
42 | -63 | 441 | -1911 | 5733 | -126126 | 21021 |
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