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A302396 Number of families of 4-subsets of an n-set that cover every element. 2
1, 0, 0, 0, 1, 26, 32596, 34359509614, 1180591620442534312297, 85070591730234605240519066638188154620, 1645504557321206042154968331851433202636630333819989444275003856 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
Number of simple 4-uniform hypergraphs of order n without isolated vertices.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Brendan McKay, Apr 07 2018
STATUS
approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)