Pyramid #191
Generating function
$$U_{191}(x, y) = \frac{y - \sqrt{2 x y \sqrt{1 - 4 y} - 2 x y + y^{2}}}{2 x y}$$
Explicit formula
$$T_{191}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$
Data table
1 1 2 5 14 42 132
1 2 5 14 42 132 429
2 6 18 56 18 594 2002
5 2 7 24 825 286 1001
14 7 28 105 385 14014 5096
42 252 1134 462 18018 68796 259896
132 924 462 20328 84084 336336 1319472
Export
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