OFFSET
0,2
COMMENTS
Equivalently, the number of partial orders (on some subset of the powerset of {1,2,...,n} ordered by set inclusion) that contain a greatest element.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..11
FORMULA
a(n) = Sum_{k=0..n} C(n,k)*2^(2^k-1).
a(n) = 2^(2^n) - A246537(n).
EXAMPLE
a(2) = 13 because there are 16 families of subsets of {1,2}. All of these contain their union except: {}, {{1},{2}}, {{},{1},{2}}. 16-3=13.
MATHEMATICA
nn = 9; Table[Sum[Binomial[n, i] 2^(2^i - 1), {i, 0, n}], {n, 0, nn}]
PROG
(PARI) a(n)=sum(k=0, n, binomial(n, k)*2^(2^k-1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Aug 25 2014
STATUS
approved