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

0,5

Comments

Number of simple 3-uniform hypergraphs without isolated vertices.

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Column 3 of A299471.

Cf. A302394.

Sequence in context: A336800 A083816 A233092 * A243818 A278864 A281285

Adjacent sequences: A302371 A302372 A302373 * A302375 A302376 A302377

Keyword

nonn,easy

Author

Brendan McKay, Apr 07 2018

Status

approved