Pyramid #805
Generating function
$$U_{805}(x, y) = \frac{\left(1 - y\right)^{4} \left(- \frac{2 x}{\left(1 - y\right)^{2}} - \sqrt{- \frac{4 x}{\left(1 - y\right)^{2}} + 1} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{805}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{m + 2 n - 1}{m}}}{k + n}$$
Data table
1 0 0 0 0 0 0
2 4 6 8 1 12 14
5 2 5 1 175 28 42
14 84 294 784 1764 3528 6468
42 336 1512 504 1386 33264 72072
132 132 726 2904 9438 264264 66066
429 5148 33462 156156 585585 1873872 5309304
Export
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