Pyramid #391
Generating function
$$U_{391}(x, y) = \frac{\left(y + 1\right)^{2}}{2} - \frac{\sqrt{4 x \left(y + 1\right)^{2} + \left(y + 1\right)^{4}}}{2}$$
Explicit formula
$$T_{391}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{2 k - 2 n}{m}} {\binom{k - n - 1}{n - 1}}}{n} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 0 0 0 0 0 0
1 -2 3 -4 5 -6 7
-2 8 -2 4 -7 112 -168
5 -3 105 -28 63 -126 231
-14 112 -504 168 -462 11088 -24024
42 -42 231 -924 3003 -84084 21021
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