Pyramid #356
Generating function
$$U_{356}(x, y) = \frac{y}{2} - \frac{\sqrt{4 x + \left(y + 1\right)^{2}}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{356}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{m + n}{m}} {\binom{k - n - 1}{m + n - 1}}}{m + n} \end{cases} $$
Data table
0 0 0 0 0 0 0
-1 1 -1 1 -1 1 -1
1 -3 6 -1 15 -21 28
-2 1 -3 7 -14 252 -42
5 -35 14 -42 105 -231 462
-14 126 -63 231 -693 18018 -42042
42 -462 2772 -12012 42042 -126126 336336
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