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A306000
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Number of labeled intersecting set-systems with no singletons covering some subset of {1,...,n}.
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3
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1, 1, 2, 16, 864, 1150976, 899934060544, 291136684662192699604992, 14704020783497694096990514485197495566069661696, 12553242487939982849962414795232892198542733625222671042878037323112413463887484853594095616
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OFFSET
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0,3
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COMMENTS
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An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. A singleton is an edge containing only one vertex.
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LINKS
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FORMULA
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EXAMPLE
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The a(3) = 16 set-systems:
{}
{{1,2}}
{{1,3}}
{{2,3}}
{{1,2,3}}
{{1,2},{1,3}}
{{1,2},{2,3}}
{{1,3},{2,3}}
{{1,2},{1,2,3}}
{{1,3},{1,2,3}}
{{2,3},{1,2,3}}
{{1,2},{1,3},{2,3}}
{{1,2},{1,3},{1,2,3}}
{{1,2},{2,3},{1,2,3}}
{{1,3},{2,3},{1,2,3}}
{{1,2},{1,3},{2,3},{1,2,3}}
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CROSSREFS
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Cf. A001206, A006126, A051185, A048143, A058891, A305001, A305843, A305844, A305854-A305857, A305935, A305999, A306001.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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