Pyramid #802
Generating function
$$U_{802}(x, y) = \frac{- 2 x + y - \sqrt{4 x + y^{2} + y \left(- 4 x - 2\right) + 1} - 1}{2 y - 2}$$
Explicit formula
$$T_{802}(n, m, k) = \begin{cases}\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}} {\binom{m + n - 1}{m}}}{n}&\text{if n>0} ,\ \\0&\text{if n=0} \end{cases} $$
Data table
0 0 0 0 0 0 0
2 2 2 2 2 2 2
-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
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