A305935 - OEIS

A305935

Number of labeled spanning intersecting set-systems on n vertices with no singletons.

1, 0, 1, 12, 809, 1146800, 899927167353, 291136684655893185321964, 14704020783497694096988185391720223222562121969, 12553242487939982849962414795232892198542733492886483991398790450208264017757788101836749760

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

An intersecting set-system S is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. S is spanning if every vertex is contained in some edge. A singleton is an edge containing only one vertex.

LINKS

Table of n, a(n) for n=0..9.

FORMULA

a(n) = A305843(n) - n * A003465(n-1).

Inverse binomial transform of A306000. - Andrew Howroyd, Aug 12 2019

EXAMPLE

The a(3) = 12 spanning intersecting set-systems with no singletons:

{{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, A305999, A306000, A306001, A306008.

Sequence in context: A155813 A220119 A178023 * A228182 A356186 A003748

Adjacent sequences: A305932 A305933 A305934 * A305936 A305937 A305938

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 15 2018

EXTENSIONS

a(6)-a(8) from Giovanni Resta, Jun 20 2018

a(9) from Andrew Howroyd, Aug 12 2019

STATUS

approved