A246537 The number of collections F of subsets of {1,2,...,n} such that the union of F is not an element of F.

1, 1, 3, 97, 32199, 2147318437, 9223372023969379707, 170141183460469231667123699412802366921, 57896044618658097711785492504343953925273862865136528165617039157077296866063

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

Cf. A246418.

Sequence in context: A243155 A201843 A278202 * A057014 A334723 A167582

Adjacent sequences: A246534 A246535 A246536 * A246538 A246539 A246540

Keyword

nonn

Author

Geoffrey Critzer, Aug 28 2014

Status

approved