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

0,6

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Column 4 of A299471.

Cf. A302394.

Sequence in context: A359054 A359052 A209961 * A208186 A316677 A092212

Adjacent sequences: A302393 A302394 A302395 * A302397 A302398 A302399

Keyword

nonn,easy

Author

Brendan McKay, Apr 07 2018

Status

approved