A375555 Triangle read by rows: T(n, k) = abs(A181937(k, n)), where A181937 are the André numbers, for 0 <= k <= n.
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 3, 1, 1, 1, 16, 9, 4, 1, 1, 1, 61, 19, 14, 5, 1, 1, 1, 272, 99, 34, 20, 6, 1, 1, 1, 1385, 477, 69, 55, 27, 7, 1, 1, 1, 7936, 1513, 496, 125, 83, 35, 8, 1, 1, 1, 50521, 11259, 2896, 251, 209, 119, 44, 9, 1
Offset: 0
Examples
Triangle starts: [0] 1; [1] 1, 1; [2] 1, 1, 1; [3] 1, 1, 2, 1; [4] 1, 1, 5, 3, 1; [5] 1, 1, 16, 9, 4, 1; [6] 1, 1, 61, 19, 14, 5, 1; [7] 1, 1, 272, 99, 34, 20, 6, 1; [8] 1, 1, 1385, 477, 69, 55, 27, 7, 1; [9] 1, 1, 7936, 1513, 496, 125, 83, 35, 8, 1; . Seen as an array: [0] 1, 1, 1, 1, 1, 1, 1, 1, ... [1] 1, 1, 2, 3, 4, 5, 6, 7, ... [2] 1, 1, 5, 9, 14, 20, 27, 35, ... [3] 1, 1, 16, 19, 34, 55, 83, 119, ... [4] 1, 1, 61, 99, 69, 125, 209, 329, ... [5] 1, 1, 272, 477, 496, 251, 461, 791, ... [6] 1, 1, 1385, 1513, 2896, 2300, 923, 1715, ... [7] 1, 1, 7936, 11259, 11056, 15775, 10284, 3431, ...
Crossrefs
Programs
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Maple
Andre := proc(n, k) option remember; local j; ifelse(k = 0, 1, ifelse(n = 0, 1, -add(binomial(k, j) * Andre(n, j), j = 0..k-1, n))) end: T := (n, k) -> abs(Andre(k, n)): seq(seq(T(n, k), k = 0..n), n = 0..10);
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Mathematica
Andre[n_, k_] := Andre[n, k] = If[k <= 0, 1, If[n == 0, 1, -Sum[Binomial[k, j] Andre[n, j], {j, 0, k-1, n}]]]; (* Seen as an array: *) A[n_, k_] := Abs[Andre[k, n + k]]; Table[A[n, k], {n, 0, 9}, {k, 0, 7}] // MatrixForm
Comments