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 A355147 #13 Jul 06 2022 17:43:27 %S A355147 1,1,1,1,1,2,1,1,3,2,1,4,5,2,1,5,9,6,1,1,6,14,15,7,1,1,7,20,29,22,8,1, %T A355147 1,8,26,43,38,17,3,1,9,34,68,76,47,15,2,1,10,43,102,144,123,62,17,2,1, %U A355147 11,53,143,234,238,149,55,11,1,1,12,64,196,377,472,387,204,66,12,1 %N A355147 Triangle read by rows: T(n,k) is the number of product-free subsets of {1,...,n} with cardinality k; n >= 0, 0 <= k <= A028391(n). %C A355147 S is product-free if for any i,j in S, not necessarily distinct, i*j is not in S. %C A355147 For n >= 2, the alternating row sums give 0. %H A355147 Marcel K. Goh and Jonah Saks, <a href="https://arxiv.org/abs/2206.12535">Alternating-sum statistics for certain sets of integers</a>, arXiv:2206.12535 [math.CO], 2022. %e A355147 Triangle T(n,k) begins: %e A355147 n/k 0 1 2 3 4 5 6 7 8 9 %e A355147 0 1 %e A355147 1 1 %e A355147 2 1 1 %e A355147 3 1 2 1 %e A355147 4 1 3 2 %e A355147 5 1 4 5 2 %e A355147 6 1 5 9 6 1 %e A355147 7 1 6 14 15 7 1 %e A355147 8 1 7 20 29 22 8 1 %e A355147 9 1 8 26 43 38 17 3 %e A355147 10 1 9 34 68 76 47 15 2 %e A355147 11 1 10 43 102 144 123 62 17 2 %e A355147 12 1 11 53 143 234 238 149 55 11 1 %e A355147 ... %e A355147 For n=5 and k=3 the T(5,3) = 2 sets are {2,3,5} and {3,4,5}. %Y A355147 Row sums give A326489. %Y A355147 Cf. A028391. %K A355147 nonn,tabf %O A355147 0,6 %A A355147 _Marcel K. Goh_, Jun 28 2022