Pyramid #75
Generating function
$$U_{75}(x, y) = \frac{\sqrt{y \left(4 x^{2} - 8 x + 4\right) + 1} + 1}{2 x^{2} - 4 x + 2}$$
Explicit formula
$$T_{75}(n, m, k) = \begin{cases}n + 1&\text{if m=0} ,\ \\\frac{k {\binom{k - m - 1}{m - 1}} {\binom{2 k - 2 m + n - 1}{n}}}{m} \end{cases} $$
Data table
1 1 -1 2 -5 14 -42
2 0 2 -8 3 -112 42
3 0 -1 12 -75 392 -189
4 0 0 -8 1 -784 504
5 0 0 2 -75 98 -882
6 0 0 0 3 -784 10584
7 0 0 0 -5 392 -882
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