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
KEYWORD
nonn,easy
AUTHOR
Brendan McKay, Apr 07 2018
STATUS
approved