OFFSET
0,3
COMMENTS
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.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..11
FORMULA
a(n) = 2^(2^n) - Sum_{k=0..n} C(n,k)*2^(2^k-1).
a(n) = 2^(2^n) - A246418(n).
EXAMPLE
a(2) = 3 because we have: {}, {{1},{2}}, {{},{1},{2}}.
MATHEMATICA
Table[2^(2^n) - Sum[Binomial[n, k] 2^(2^k - 1), {k, 0, n}], {n, 0,
10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Aug 28 2014
STATUS
approved