Pyramid #881
Generating function
$$U_{881}(x, y) = \frac{\left(2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x \left(y + 1\right)}}{2} \right)}}{3} \right)}\right) \left(y + 1\right)^{2}}{3 x}$$
Explicit formula
$$T_{881}(n, m, k) = \frac{k {\binom{3 k + n}{m}} {\binom{2 k + 3 n - 1}{n}}}{k + n}$$
Data table
1 3 3 1 0 0 0
2 8 12 8 2 0 0
7 35 7 7 35 7 0
3 18 45 6 45 18 3
143 1001 3003 5005 5005 3003 1001
728 5824 20384 40768 5096 40768 20384
3876 34884 139536 325584 488376 488376 325584
Export
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