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%I #16 Jul 06 2022 17:42:50
%S 1,1,1,1,2,1,1,3,3,1,1,4,5,2,1,5,9,7,2,1,6,11,8,2,1,7,17,19,10,2,1,8,
%T 21,25,14,3,1,9,27,37,24,6,1,10,31,42,26,6,1,11,41,73,68,32,6,1,12,45,
%U 79,72,33,6,1,13,57,124,151,105,39,6,1,14,63,138,167,114,41,6
%N Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which every pair of elements is coprime; n >= 0, 0 <= k <= A036234(n).
%C For n >= 1, the alternating row sums equal 0.
%H 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 Triangle T(n,k) begins:
%e n/k 0 1 2 3 4 5 6
%e 0 1
%e 1 1 1
%e 2 1 2 1
%e 3 1 3 3 1
%e 4 1 4 5 2
%e 5 1 5 9 7 2
%e 6 1 6 11 8 2
%e 7 1 7 17 19 10 2
%e 8 1 8 21 25 14 3
%e 9 1 9 27 37 24 6
%e 10 1 10 31 42 26 6
%e 11 1 11 41 73 68 32 6
%e 12 1 12 45 79 72 33 6
%e ...
%e For n=8 and k=5 the T(8,5)=3 sets are {1,2,3,5,7}, {1,3,4,5,7}, and {1,3,5,7,8}.
%Y Row sums give A084422.
%Y Cf. A000720, A036234, A186974, A320436.
%K nonn,tabf
%O 0,5
%A _Marcel K. Goh_, Jun 27 2022
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