Pyramid #140
Generating function
$$U_{140}(x, y) = \frac{- y + \sqrt{4 x + y^{2} + y \left(4 x + 2\right) + 1} - 1}{2 x y + 2 x}$$
Explicit formula
$$T_{140}(n, m, k) = \frac{\left(-1\right)^{m + n} k {\binom{k + 2 n - 1}{n}} {\binom{k + m + n - 1}{m}}}{k + n}$$
Data table
1 -1 1 -1 1 -1 1
-1 2 -3 4 -5 6 -7
2 -6 12 -2 3 -42 56
-5 2 -5 1 -175 28 -42
14 -7 21 -49 98 -1764 294
-42 252 -882 2352 -5292 10584 -19404
132 -924 3696 -11088 2772 -60984 121968
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