Pyramid #281
Generating function
$$U_{281}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{2} - 4\right) + 1}}{2 y}$$
Explicit formula
$$T_{281}(n, m, k) = \frac{k \left(\left(-1\right)^{n} + 1\right) {\binom{k + m}{\frac{n}{2}}} {\binom{k + 2 m - 1}{m}}}{2 k + 2 m}$$
Data table
1 1 2 5 14 42 132
0 0 0 0 0 0 0
1 2 6 2 7 252 924
0 0 0 0 0 0 0
0 1 6 3 14 63 2772
0 0 0 0 0 0 0
0 0 2 2 14 84 462
Export
expand_less