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A371830
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Irregular triangle read by rows: T(n,k) is the number of unlabeled n-vertex hypergraphs (or set systems) with k hyperedges (none of which is empty), 0 <= k <= 2^n-1.
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2
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1, 1, 1, 1, 2, 2, 1, 1, 3, 6, 10, 10, 6, 3, 1, 1, 4, 13, 39, 97, 187, 290, 365, 365, 290, 187, 97, 39, 13, 4, 1, 1, 5, 23, 111, 514, 2160, 8035, 26195, 74382, 183710, 395498, 744592, 1229846, 1787148, 2289929, 2591163, 2591163, 2289929, 1787148, 1229846, 744592, 395498, 183710, 74382, 26195, 8035, 2160, 514, 111, 23, 5, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n,k) = Sum_{j=0..k} (-1)^(k-j)*A052265(n,j).
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EXAMPLE
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Triangle begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---+-----------------------------------------------------
0 | 1
1 | 1 1
2 | 1 2 2 1
3 | 1 3 6 10 10 6 3 1
4 | 1 4 13 39 97 187 290 365 365 290 187 97 39 13 4 1
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PROG
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(SageMath)
return sum(1 for G in hypergraphs.nauty(k, n, set_min_size=1))
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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