Pyramid #170
Generating function
$$U_{170}(x, y) = \frac{- 2 x y - x - \sqrt{x^{2} - 4 x y - 2 x + 1} + 1}{2 x^{2} y}$$
Explicit formula
$$T_{170}(n, m, k) = \frac{k {\binom{k + n}{m}} {\binom{k + m + n}{n}}}{k + n}$$
Data table
1 1 0 0 0 0 0
1 3 2 0 0 0 0
1 6 1 5 0 0 0
1 1 3 35 14 0 0
1 15 7 14 126 42 0
1 21 14 42 63 462 132
1 28 252 105 231 2772 1716
Export
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