Generating function
$$U_{448}(x, y) = x + \frac{\sqrt{\frac{4 x}{\left(1 - y\right)^{3}} + \frac{1}{\left(1 - y\right)^{6}}}}{2} + \frac{1}{2 \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{448}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}}}{n}&\text{if n>0 and m=0} ,\ \\\frac{3 \left(-1\right)^{m - 1} k {\binom{- 3 k + 3 n - 1}{m - 1}} {\binom{2 k - n - 1}{n}}}{m} \end{cases} $$
1 | 3 | 6 | 1 | 15 | 21 | 28 |
2 | 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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