Pyramid #46
Generating function
$$U_{46}(x, y) = \frac{x + \sqrt{x^{2} - 2 x + y \left(4 x - 4\right) + 1} - 1}{y \left(2 x - 2\right)}$$
Explicit formula
$$T_{46}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + m + n - 1}{n}}}{k + 2 m}$$
Data table
1 1 2 5 14 42 132
1 2 6 2 7 252 924
1 3 12 5 21 882 3696
1 4 2 1 49 2352 11088
1 5 3 175 98 5292 2772
1 6 42 28 1764 10584 60984
1 7 56 42 294 19404 121968
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