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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 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

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