The OEIS is supported by the many generous donors to the OEIS Foundation.

The number of collections F of subsets of {1,2,...,n} such that the union of F is not an element of F.

2

`%I #8 Aug 28 2014 20:05:57
`

`%S 1,1,3,97,32199,2147318437,9223372023969379707,
`

`%T 170141183460469231667123699412802366921,
`

`%U 57896044618658097711785492504343953925273862865136528165617039157077296866063
`

`%N The number of collections F of subsets of {1,2,...,n} such that the union of F is not an element of F.
`

`%C Equivalently, the number of partial orders (on some subset of the powerset of {1,2,...,n} ordered by set inclusion) that contain no maximal elements (the empty family) or at least two maximal elements.
`

`%H Alois P. Heinz, <a href="/A246537/b246537.txt">Table of n, a(n) for n = 0..11</a>
`

`%F a(n) = 2^(2^n) - Sum_{k=0..n} C(n,k)*2^(2^k-1).
`

`%F a(n) = 2^(2^n) - A246418(n).
`

`%e a(2) = 3 because we have: {}, {{1},{2}}, {{},{1},{2}}.
`

`%t Table[2^(2^n) - Sum[Binomial[n, k] 2^(2^k - 1), {k, 0, n}], {n, 0,
`

`%t 10}]
`

`%Y Cf. A246418.
`

`%K nonn
`

`%O 0,3
`

`%A _Geoffrey Critzer_, Aug 28 2014
`