A302396 Number of families of 4-subsets of an n-set that cover every element.

1, 0, 0, 0, 1, 26, 32596, 34359509614, 1180591620442534312297, 85070591730234605240519066638188154620, 1645504557321206042154968331851433202636630333819989444275003856

Offset: 0

Author

Brendan McKay, Apr 07 2018

Keywords

• nonn
• easy

Comments

Number of simple 4-uniform hypergraphs of order n without isolated vertices.

Examples

			For n=5 all families with at least two 4-sets will cover every element.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..18

Crossrefs

Column 4 of A299471.

Cf. A302394.

Programs

GAP

Flat(List([0..10],n->Sum([0..n],k->(-1)^k*Binomial(n,k)*2^Binomial(n-k,4)))); # Muniru A Asiru, Apr 07 2018

Maple

seq(add((-1)^k * binomial(n,k) * 2^binomial(n-k,4), k = 0..n), n=0..12)

Mathematica

Array[Sum[(-1)^k*Binomial[#, k] 2^Binomial[# - k, 4], {k, 0, #}] &, 11, 0] (* Michael De Vlieger, Apr 07 2018 *)

PARI

a(n) = sum(k=0, n, (-1)^k*binomial(n,k)*2^binomial(n-k,4)); \\ Michel Marcus, Apr 07 2018

Formula

a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k) * 2^binomial(n-k,4).