Pyramid #64
Generating function
$$U_{64}(x, y) = \frac{- x + \sqrt{x^{2} + 2 y \sqrt{1 - 4 x} + y \left(4 x - 2\right)}}{y \left(\sqrt{1 - 4 x} - 1\right)}$$
Explicit formula
$$T_{64}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + 2 m + 2 n - 1}{n}}}{k + 2 m + n}$$
Data table
1 1 2 5 14 42 132
1 3 1 35 126 462 1716
2 9 4 175 756 3234 13728
5 28 15 77 3822 1848 87516
14 9 55 3185 1764 94248 48906
42 297 2002 1274 77112 447678 2510508
132 1001 728 4998 325584 2027718 12156144
Export
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