Pyramid #389
Generating function
$$U_{389}(x, y) = \frac{1 - \sqrt{- 4 x y^{4} - 16 x y^{3} - 24 x y^{2} - 16 x y - 4 x + 1}}{2 x y^{2} + 4 x y + 2 x}$$
Explicit formula
$$T_{389}(n, m, k) = \frac{k {\binom{2 k + 4 n}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
Data table
1 2 1 0 0 0 0
1 6 15 2 15 6 1
2 2 9 24 42 504 42
5 7 455 182 5005 1001 15015
14 252 2142 11424 4284 119952 259896
42 924 9702 6468 30723 1106028 3133746
132 3432 429 3432 19734 868296 3039036
Export
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