Pyramid #106
Generating function
$$U_{106}(x, y) = \frac{x^{2} + y^{2} + y \left(- 2 x - 2\right) + \left(- x + y - 1\right) \sqrt{x^{2} - 2 x + y^{2} + y \left(- 2 x - 2\right) + 1} + 1}{2 x^{2}}$$
Explicit formula
$$T_{106}(n, m, k) = \frac{2 k {\binom{2 k + m + n}{m}} {\binom{m + n - 1}{n}}}{2 k + m + n}$$
Data table
1 2 3 4 5 6 7
0 2 8 2 4 7 112
0 2 15 6 175 42 882
0 2 24 14 56 1764 4704
0 2 35 28 147 588 19404
0 2 48 504 336 16632 66528
0 2 63 84 693 4158 198198
Export
expand_less