Pyramid #296
Generating function
$$U_{296}(x, y) = \frac{\sqrt{3} \left(\sqrt{3} \sqrt{x} - \sqrt{- 8 \sqrt{3} \sqrt{x} y \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)} + 3 x}\right)}{6 \sqrt{x} y}$$
Explicit formula
$$T_{296}(n, m, k) = \frac{k {\binom{k + 2 m - 1}{m}} {\binom{k + m + 3 n - 1}{n}}}{k + m + 2 n}$$
Data table
1 1 2 5 14 42 132
1 2 6 2 7 252 924
3 7 24 9 35 1386 5544
12 3 11 44 182 7644 3234
55 143 546 2275 98 4284 188496
273 728 2856 1224 54264 244188 1106028
1428 3876 15504 6783 30723 1413258 6545616
Export
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