

A302374


Number of families of 3subsets of an nset that cover every element.


16



1, 0, 0, 1, 11, 958, 1042642, 34352419335, 72057319189324805, 19342812465316957316575404, 1329227995591487745008054001085455444, 46768052394574271874565344427028486133322470597757, 1684996666696914425950059707959735374604894792118382485311245761903
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OFFSET

0,5


COMMENTS

Number of simple 3uniform hypergraphs without isolated vertices.


LINKS

Table of n, a(n) for n=0..12.


FORMULA

a(n) = Sum_{k=0..n} (1)^k * binomial(n,k) * 2^binomial(nk,3).


EXAMPLE

For n=3, all families with at least two 3subsets will cover every element.


MAPLE

seq(add((1)^k * binomial(n, k) * 2^binomial(nk, 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(nk, 3)); \\ Michel Marcus, Apr 07 2018
(GAP) Flat(List([0..12], n>Sum([0..n], k>(1)^k*Binomial(n, k)*2^Binomial(nk, 3)))); # Muniru A Asiru, Apr 07 2018


CROSSREFS

Cf. A302394.
Sequence in context: A176709 A083816 A233092 * A243818 A278864 A281285
Adjacent sequences: A302371 A302372 A302373 * A302375 A302376 A302377


KEYWORD

nonn,easy


AUTHOR

Brendan McKay, Apr 07 2018


STATUS

approved



