Pyramid #33
Generating function
$$U_{33}(x, y) = \frac{- x^{3} + 3 x^{2} - 3 x + \left(x - 1\right) \sqrt{x^{4} - 4 x^{3} + 6 x^{2} - 4 x - 4 y + 1} + 1}{2 y}$$
Explicit formula
$$T_{33}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + 4 m + n - 1}{n}}}{k + 2 m}$$
Data table
1 1 2 5 14 42 132
1 5 18 65 238 882 33
1 15 9 455 2142 9702 429
1 35 33 2275 13566 74382 3861
1 7 99 91 6783 446292 27027
1 126 2574 3094 284886 223146 1567566
1 21 6006 9282 1044582 966966 783783
Export
expand_less