Pyramid #73
Generating function
$$U_{73}(x, y) = \frac{\sqrt{4 x y^{2} - 8 x y + 4 x + 1} + 1}{2 y^{2} - 4 y + 2}$$
Explicit formula
$$T_{73}(n, m, k) = \begin{cases}{\binom{2 k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{k {\binom{k - n - 1}{n - 1}} {\binom{2 k + m - 2 n - 1}{m}}}{n}&\text{if n>0} \end{cases} $$
Data table
1 2 3 4 5 6 7
1 0 0 0 0 0 0
-1 2 -1 0 0 0 0
2 -8 12 -8 2 0 0
-5 3 -75 1 -75 3 -5
14 -112 392 -784 98 -784 392
-42 42 -189 504 -882 10584 -882
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