%I
%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^k1).
%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
