Generating function
$$U_{181}(x, y) = \frac{x^{2} + 2 x - \sqrt{\left(x + 1\right) \left(x^{3} + 3 x^{2} + 3 x + 4 y + 1\right)} + 1}{y \left(2 x + 2\right)}$$
Explicit formula
$$T_{181}(n, m, k) = \frac{\left(-1\right)^{- k - m + n} k {\binom{k + 2 m - 1}{m}} {\binom{2 k + 3 m + n - 1}{n}}}{k + m}$$
-1 | 1 | -2 | 5 | -14 | 42 | -132 |
2 | -5 | 16 | -55 | 196 | -714 | 2640 |
-3 | 15 | -72 | 330 | -1470 | 6426 | -27720 |
4 | -35 | 24 | -1430 | 7840 | -40698 | 203280 |
-5 | 7 | -66 | 5005 | -33320 | 203490 | -1168860 |
6 | -126 | 1584 | -15015 | 119952 | -854658 | 5610528 |
-7 | 21 | -3432 | 4004 | -379848 | 3133746 | -23377200 |
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