login
A246418
Number of collections F of subsets of {1,2,...,n} whose union is itself an element of F.
2
1, 3, 13, 159, 33337, 2147648859, 9223372049740171909, 170141183460469231796250908018965844535, 57896044618658097711785492504343953927996121800504035873840544850835832773873
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
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
Cf. A246537.
Sequence in context: A014376 A224990 A065622 * A140421 A176315 A290758
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Aug 25 2014
STATUS
approved