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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).

%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