Pyramid #907
Generating function
$$U_{907}(x, y) = \frac{\sqrt{- 4 x y^{2} - 16 x y - 16 x + 1} + 1}{2 y + 4}$$
Explicit formula
$$T_{907}(n, m, k) = \begin{cases}1&\text{if n=0, m=0} ,\ \\-2&\text{if 2*n-k=0, m=0 } ,\ \\0&\text{if 2*n-k=0, m>0} ,\ \\- \frac{2^{- k - m + 2 n} k {\binom{- k + 2 n}{m}} {\binom{- k + 2 n}{n}}}{- k + 2 n} \end{cases} $$
Data table
1 -0.25 0.125 -0.0625 0.03125 -0.015625 0.0078125
-2 -1 0 0 0 0 0
-8 -12 -6 -1 0 0 0
-64 -16 -16 -8 -2 -2 0
-64 -224 -336 -28 -14 -42 -7
-7168 -32256 -64512 -75264 -56448 -28224 -9408
-86016 -473088 -118272 -177408 -177408 -1241856 -620928
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