Pyramid #528
Generating function
$$U_{528}(x, y) = - \frac{\sqrt{4 x \left(1 - y\right)^{2} + \frac{1}{\left(1 - y\right)^{2}}}}{2} + \frac{1}{2 - 2 y}$$
Explicit formula
$$T_{528}(n, m, k) = \begin{cases}0&\text{if n<k } ,\ \\- \frac{k {\binom{k - n - 1}{n - 1}} {\binom{k + m - 4 n - 1}{m}}}{n} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 3 -3 1 0 0 0
1 -7 21 -35 35 -21 7
-2 22 -11 33 -66 924 -924
5 -75 525 -2275 6825 -15015 25025
-14 266 -2394 13566 -54264 162792 -379848
42 -966 10626 -74382 37191 -1413258 4239774
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