A306000 Number of labeled intersecting set-systems with no singletons covering some subset of {1,...,n}.

1, 1, 2, 16, 864, 1150976, 899934060544, 291136684662192699604992, 14704020783497694096990514485197495566069661696, 12553242487939982849962414795232892198542733625222671042878037323112413463887484853594095616

Offset: 0

Author

Gus Wiseman, Jun 16 2018

Keywords

• nonn

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.

Examples

			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}}
		

Crossrefs

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

Formula

a(n) = A051185(n) - n*2^(2^(n-1)-1). - Andrew Howroyd, Aug 12 2019

Extensions

a(6)-a(9) from Andrew Howroyd, Aug 12 2019