A246418 Number of collections F of subsets of {1,2,...,n} whose union is itself an element of F.

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

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

Cf. A246537.

Sequence in context: A014376 A224990 A065622 * A140421 A176315 A290758

Adjacent sequences: A246415 A246416 A246417 * A246419 A246420 A246421

Keyword

nonn

Author

Geoffrey Critzer, Aug 25 2014

Status

approved