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A306000
Number of labeled intersecting set-systems with no singletons covering some subset of {1,...,n}.
3
1, 1, 2, 16, 864, 1150976, 899934060544, 291136684662192699604992, 14704020783497694096990514485197495566069661696, 12553242487939982849962414795232892198542733625222671042878037323112413463887484853594095616
OFFSET
0,3
COMMENTS
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.
FORMULA
a(n) = A051185(n) - n*2^(2^(n-1)-1). - Andrew Howroyd, Aug 12 2019
EXAMPLE
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}}
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 16 2018
EXTENSIONS
a(6)-a(9) from Andrew Howroyd, Aug 12 2019
STATUS
approved