Pyramid #359
Generating function
$$U_{359}(x, y) = \frac{- x - 2 y - \sqrt{x^{2} - 2 x + y \left(4 x - 4\right) + 1} + 1}{2 y^{2}}$$
Explicit formula
$$T_{359}(n, m, k) = \frac{k {\binom{2 k + 2 m}{m}} {\binom{k + m + n - 1}{n}}}{k + m}$$
Data table
1 2 5 14 42 132 429
1 4 15 56 21 792 3003
1 6 3 14 63 2772 12012
1 8 5 28 147 7392 36036
1 1 75 49 294 16632 9009
1 12 105 784 5292 33264 198198
1 14 14 1176 882 60984 396396
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