A302374 Number of families of 3-subsets of an n-set that cover every element.

1, 0, 0, 1, 11, 958, 1042642, 34352419335, 72057319189324805, 19342812465316957316575404, 1329227995591487745008054001085455444, 46768052394574271874565344427028486133322470597757, 1684996666696914425950059707959735374604894792118382485311245761903

Offset: 0

Author

Brendan McKay, Apr 07 2018

Keywords

• nonn
• easy

Comments

Number of simple 3-uniform hypergraphs without isolated vertices.

Examples

			For n=3, all families with at least two 3-subsets will cover every element.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..25

Crossrefs

Column 3 of A299471.

Cf. A302394.

Programs

GAP

Flat(List([0..12],n->Sum([0..n],k->(-1)^k*Binomial(n,k)*2^Binomial(n-k,3)))); # Muniru A Asiru, Apr 07 2018

Maple

seq(add((-1)^k * binomial(n,k) * 2^binomial(n-k,3), k = 0..n), n=0..15);

Mathematica

Array[Sum[(-1)^k*Binomial[#, k] 2^Binomial[# - k, 3], {k, 0, #}] &, 13, 0] (* Michael De Vlieger, Apr 07 2018 *)

PARI

a(n) = sum(k=0, n, (-1)^k*binomial(n,k)*2^binomial(n-k,3)); \\ Michel Marcus, Apr 07 2018

Formula

a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k) * 2^binomial(n-k,3).