Pyramid #210
Generating function
$$U_{210}(x, y) = \frac{1 - \sqrt{y \left(- 4 x^{3} - 12 x^{2} - 12 x - 4\right) + 1}}{y \left(2 x + 2\right)}$$
Explicit formula
$$T_{210}(n, m, k) = \frac{k {\binom{2 k + 3 m}{n}} {\binom{k + 2 m - 1}{m}}}{k + m}$$
Data table
1 1 2 5 14 42 132
2 5 16 55 196 714 264
1 1 56 275 1274 5712 2508
0 1 112 825 5096 2856 15048
0 5 14 165 14014 9996 63954
0 1 112 231 28028 259896 2046528
0 0 56 231 42042 519792 511632
Export
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