Pyramid #80
Pyramid #81
Pyramid #82
Generating function
$$U_{81}(x, y) = \frac{- 2 x y - 2 x - \sqrt{- 4 x y - 4 x + 1} + 1}{2 x^{2} \left(y + 1\right)}$$
Explicit formula
$$T_{81}(n, m, k) = \frac{k {\binom{k + n}{m}} {\binom{2 k + 2 n}{n}}}{k + n}$$
Data table
1 1 0 0 0 0 0
2 4 2 0 0 0 0
5 15 15 5 0 0 0
14 56 84 56 14 0 0
42 21 42 42 21 42 0
132 792 198 264 198 792 132
429 3003 9009 15015 15015 9009 3003
Related
Pyramid #387: Change x y
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