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A302374 Number of families of 3-subsets of an n-set that cover every element. 17
1, 0, 0, 1, 11, 958, 1042642, 34352419335, 72057319189324805, 19342812465316957316575404, 1329227995591487745008054001085455444, 46768052394574271874565344427028486133322470597757, 1684996666696914425950059707959735374604894792118382485311245761903 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Number of simple 3-uniform hypergraphs without isolated vertices.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Brendan McKay, Apr 07 2018
STATUS
approved

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Last modified July 23 19:43 EDT 2024. Contains 374553 sequences. (Running on oeis4.)