Pyramid #898
Generating function
$$U_{898}(x, y) = \frac{2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2 \operatorname{abs}{\left(y - 1 \right)}} \right)}}{3} \right)}}{3 x}$$
Explicit formula
$$T_{898}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{2 k + m + 2 n - 1}{m}}}{k + n}$$
Data table
1 2 3 4 5 6 7
2 8 2 4 7 112 168
7 42 147 392 882 1764 3234
3 24 108 36 99 2376 5148
143 143 7865 3146 102245 286286 715715
728 8736 56784 264992 99372 3179904 9009728
3876 54264 40698 217056 922488 33209568 105163632
Export
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