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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, 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
0,9
COMMENTS
See A181937 for comments and references.
EXAMPLE
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, ...
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);
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
CROSSREFS
Cf. A181937, A375554 (row sums), A030662 (central terms, main diagonal of array), A010763 (central terms of the (1, 1)-based variant).
Sequence in context: A256384 A111673 A121391 * A347615 A241194 A352893
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 19 2024
STATUS
approved