Generating function
$$U_{389}(x, y) = \frac{1 - \sqrt{- 4 x y^{4} - 16 x y^{3} - 24 x y^{2} - 16 x y - 4 x + 1}}{2 x y^{2} + 4 x y + 2 x}$$
Explicit formula
$$T_{389}(n, m, k) = \frac{k {\binom{2 k + 4 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
1 | 6 | 15 | 2 | 15 | 6 | 1 |
2 | 2 | 9 | 24 | 42 | 504 | 42 |
5 | 7 | 455 | 182 | 5005 | 1001 | 15015 |
14 | 252 | 2142 | 11424 | 4284 | 119952 | 259896 |
42 | 924 | 9702 | 6468 | 30723 | 1106028 | 3133746 |
132 | 3432 | 429 | 3432 | 19734 | 868296 | 3039036 |
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