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A246537 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

%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

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)