Pyramid #71
Generating function
$$U_{71}(x, y) = \frac{y^{2} - 2 y - \sqrt{- 4 x + y^{4} - 4 y^{3} + 6 y^{2} - 4 y + 1} + 1}{2 x}$$
Explicit formula
$$T_{71}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{2 k + m + 4 n - 1}{m}}}{k + n}$$
Data table
1 2 3 4 5 6 7
1 6 21 56 126 252 462
2 2 11 44 143 4004 1001
5 7 525 28 119 4284 13566
14 252 2394 1596 8379 368676 1413258
42 924 10626 85008 5313 276276 1243242
132 3432 46332 432432 3135132 18810792 97189092
Export
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