Pyramid #387
Generating function
$$U_{387}(x, y) = \frac{- y \left(2 x + 2\right) - \sqrt{y \left(- 4 x - 4\right) + 1} + 1}{y^{2} \left(2 x + 2\right)}$$
Explicit formula
$$T_{387}(n, m, k) = \frac{k {\binom{k + m}{n}} {\binom{2 k + 2 m}{m}}}{k + m}$$
Data table
1 2 5 14 42 132 429
1 4 15 56 21 792 3003
0 2 15 84 42 198 9009
0 0 5 56 42 264 15015
0 0 0 14 21 198 15015
0 0 0 0 42 792 9009
0 0 0 0 0 132 3003
Export
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