Pyramid #297
Generating function
$$U_{297}(x, y) = \frac{\sqrt{3} \left(\sqrt{3} \sqrt{y} - \sqrt{- 8 \sqrt{3} x \sqrt{y} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + 3 y}\right)}{6 x \sqrt{y}}$$
Explicit formula
$$T_{297}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{k + 3 m + n - 1}{m}}}{k + 2 m + n}$$
Data table
1 1 3 12 55 273 1428
1 2 7 3 143 728 3876
2 6 24 11 546 2856 15504
5 2 9 44 2275 1224 6783
14 7 35 182 98 54264 30723
42 252 1386 7644 4284 244188 1413258
132 924 5544 3234 188496 1106028 6545616
Export
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