This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375555 #7 Aug 25 2024 04:24:16
%S A375555 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,
%T A375555 99,34,20,6,1,1,1,1385,477,69,55,27,7,1,1,1,7936,1513,496,125,83,35,8,
%U A375555 1,1,1,50521,11259,2896,251,209,119,44,9,1
%N A375555 Triangle read by rows: T(n, k) = abs(A181937(k, n)), where A181937 are the André numbers, for 0 <= k <= n.
%C A375555 See A181937 for comments and references.
%e A375555 Triangle starts:
%e A375555 [0] 1;
%e A375555 [1] 1, 1;
%e A375555 [2] 1, 1, 1;
%e A375555 [3] 1, 1, 2, 1;
%e A375555 [4] 1, 1, 5, 3, 1;
%e A375555 [5] 1, 1, 16, 9, 4, 1;
%e A375555 [6] 1, 1, 61, 19, 14, 5, 1;
%e A375555 [7] 1, 1, 272, 99, 34, 20, 6, 1;
%e A375555 [8] 1, 1, 1385, 477, 69, 55, 27, 7, 1;
%e A375555 [9] 1, 1, 7936, 1513, 496, 125, 83, 35, 8, 1;
%e A375555 .
%e A375555 Seen as an array:
%e A375555 [0] 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A375555 [1] 1, 1, 2, 3, 4, 5, 6, 7, ...
%e A375555 [2] 1, 1, 5, 9, 14, 20, 27, 35, ...
%e A375555 [3] 1, 1, 16, 19, 34, 55, 83, 119, ...
%e A375555 [4] 1, 1, 61, 99, 69, 125, 209, 329, ...
%e A375555 [5] 1, 1, 272, 477, 496, 251, 461, 791, ...
%e A375555 [6] 1, 1, 1385, 1513, 2896, 2300, 923, 1715, ...
%e A375555 [7] 1, 1, 7936, 11259, 11056, 15775, 10284, 3431, ...
%p A375555 Andre := proc(n, k) option remember; local j;
%p A375555 ifelse(k = 0, 1, ifelse(n = 0, 1,
%p A375555 -add(binomial(k, j) * Andre(n, j), j = 0..k-1, n))) end:
%p A375555 T := (n, k) -> abs(Andre(k, n)): seq(seq(T(n, k), k = 0..n), n = 0..10);
%t A375555 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}]]];
%t A375555 (* Seen as an array: *)
%t A375555 A[n_, k_] := Abs[Andre[k, n + k]];
%t A375555 Table[A[n, k], {n, 0, 9}, {k, 0, 7}] // MatrixForm
%Y A375555 Cf. A181937, A375554 (row sums), A030662 (central terms, main diagonal of array), A010763 (central terms of the (1, 1)-based variant).
%K A375555 nonn,tabl
%O A375555 0,9
%A A375555 _Peter Luschny_, Aug 19 2024