Pyramid #920
Generating function
$$U_{920}(x, y) = \frac{\sqrt{y \left(- 8 x - 8\right) + 1}}{4} + \frac{1}{4}$$
Explicit formula
$$T_{920}(n, m, k) = \begin{cases}0&\text{if m = 0, n > 0} ,\ \\2^{- k}&\text{if n = 0, m = 0} ,\ \\- \frac{2^{- k + m} k {\binom{m}{n}} {\binom{- k + 2 m - 1}{m - 1}}}{m}&\text{if m > 0} \end{cases} $$
Data table
0.5 -1 -2 -8 -4 -224 -1344
0 -1 -4 -24 -16 -112 -8064
0 0 -2 -24 -24 -224 -2016
0 0 0 -8 -16 -224 -2688
0 0 0 0 -4 -112 -2016
0 0 0 0 0 -224 -8064
0 0 0 0 0 0 -1344
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