Pyramid #866
Generating function
$$U_{866}(x, y) = \frac{1}{\left(1 - y\right)^{5} \left(- x + \frac{1}{\left(1 - y\right)^{3}}\right)}$$
Explicit formula
$$T_{866}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{2 k + m - 3 n - 1}{m}}$$
Data table
1 2 3 4 5 6 7
1 -1 0 0 0 0 0
1 -4 6 -4 1 0 0
1 -7 21 -35 35 -21 7
1 -1 45 -12 21 -252 21
1 -13 78 -286 715 -1287 1716
1 -16 12 -56 182 -4368 8008
Export
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