Pyramid #301
Generating function
$$U_{301}(x, y) = \frac{2 \sin{\left(\frac{\arcsin{\left(\sqrt{\frac{27 x}{4} + \frac{27 y}{4}} \right)}}{3} \right)}}{\sqrt{3 x + 3 y}}$$
Explicit formula
$$T_{301}(n, m, k) = \frac{k {\binom{m + n}{m}} {\binom{k + 3 m + 3 n - 1}{m + n}}}{k + 2 m + 2 n}$$
Data table
1 1 3 12 55 273 1428
1 6 36 22 1365 8568 54264
3 36 33 273 2142 162792 1211364
12 22 273 2856 27132 2422728 207207
55 1365 2142 27132 302841 3108105 30045015
273 8568 162792 2422728 3108105 36054018 388756368
1428 54264 1211364 207207 30045015 388756368 46262007792
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