A297704 Triangle read by rows, T(n,k) = binomial(n, k)*hypergeom2F1(k - n, n + 1, k + 2, -2) for n >= 0 and 0 <= k <= n.
1, 3, 1, 15, 6, 1, 93, 39, 9, 1, 645, 276, 72, 12, 1, 4791, 2073, 576, 114, 15, 1, 37275, 16242, 4689, 1020, 165, 18, 1, 299865, 131295, 38889, 8979, 1635, 225, 21, 1, 2474025, 1087080, 327960, 78888, 15510, 2448, 294, 24, 1
Offset: 0
Examples
Triangle starts: [0] 1 [1] 3, 1 [2] 15, 6, 1 [3] 93, 39, 9, 1 [4] 645, 276, 72, 12, 1 [5] 4791, 2073, 576, 114, 15, 1 [6] 37275, 16242, 4689, 1020, 165, 18, 1
Links
- Peter Luschny, row n for n = 0..44
Programs
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Mathematica
T[n_, k_] := Binomial[n, k] Hypergeometric2F1[k - n, n + 1, k + 2, -2]; Table[T[n, k], {n, 0, 6}, {k, 0, n}] // Flatten