Pyramid #949
Generating function
$$U_{949}(x, y) = \frac{- 2 x y - x - \sqrt{x^{2} - 2 x + y \left(4 x^{2} - 4 x\right) + 1} + 1}{2 x^{2} y^{2}}$$
Explicit formula
$$T_{949}(n, m, k) = \frac{k {\binom{2 k + 2 m}{m}} {\binom{k + n - 1}{- m + n}}}{k + m}$$
Data table
1 0 0 0 0 0 0
1 2 0 0 0 0 0
1 4 5 0 0 0 0
1 6 15 14 0 0 0
1 8 3 56 42 0 0
1 1 5 14 21 132 0
1 12 75 28 63 792 429
Related
Export
expand_less