Pyramid #181
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
$$T_{181}(n, m, k) = \frac{\left(-1\right)^{- k - m + n} k {\binom{k + 2 m - 1}{m}} {\binom{2 k + 3 m + n - 1}{n}}}{k + m}$$
Data table
-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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