Pyramid #848
Generating function
$$U_{848}(x, y) = \frac{1 - \sqrt{- \frac{4 x}{1 - y} + 1}}{2 x \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{848}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{4 k + m + n - 1}{m}}}{k + n}$$
Data table
1 4 1 2 35 56 84
1 5 15 35 7 126 21
2 12 42 112 252 504 924
5 35 14 42 105 231 462
14 112 504 168 462 11088 24024
42 378 189 693 2079 54054 126126
132 132 726 2904 9438 264264 66066
Export
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