Pyramid #300
Generating function
$$U_{300}(x, y) = \frac{- x - \sqrt{x^{2} - 2 x - 4 y^{2} + 1} + 1}{2 y^{2}}$$
Explicit formula
$$T_{300}(n, m, k) = \frac{k \left(\left(-1\right)^{m} + 1\right) {\binom{k + m}{\frac{m}{2}}} {\binom{k + m + n - 1}{n}}}{2 k + 2 m}$$
Data table
1 0 1 0 2 0 5
1 0 3 0 1 0 35
1 0 6 0 3 0 14
1 0 1 0 7 0 42
1 0 15 0 14 0 105
1 0 21 0 252 0 231
1 0 28 0 42 0 462
Export
expand_less