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Number of labeled intersecting set-systems with no singletons covering some subset of {1,...,n}.
3

%I #10 Aug 12 2019 23:06:13

%S 1,1,2,16,864,1150976,899934060544,291136684662192699604992,

%T 14704020783497694096990514485197495566069661696,

%U 12553242487939982849962414795232892198542733625222671042878037323112413463887484853594095616

%N Number of labeled intersecting set-systems with no singletons covering some subset of {1,...,n}.

%C 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.

%F a(n) = A051185(n) - n*2^(2^(n-1)-1). - _Andrew Howroyd_, Aug 12 2019

%e The a(3) = 16 set-systems:

%e {}

%e {{1,2}}

%e {{1,3}}

%e {{2,3}}

%e {{1,2,3}}

%e {{1,2},{1,3}}

%e {{1,2},{2,3}}

%e {{1,3},{2,3}}

%e {{1,2},{1,2,3}}

%e {{1,3},{1,2,3}}

%e {{2,3},{1,2,3}}

%e {{1,2},{1,3},{2,3}}

%e {{1,2},{1,3},{1,2,3}}

%e {{1,2},{2,3},{1,2,3}}

%e {{1,3},{2,3},{1,2,3}}

%e {{1,2},{1,3},{2,3},{1,2,3}}

%Y Cf. A001206, A006126, A051185, A048143, A058891, A305001, A305843, A305844, A305854-A305857, A305935, A305999, A306001.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jun 16 2018

%E a(6)-a(9) from _Andrew Howroyd_, Aug 12 2019