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A246537 The number of collections F of subsets of {1,2,...,n} such that the union of F is not an element of F. 2
1, 1, 3, 97, 32199, 2147318437, 9223372023969379707, 170141183460469231667123699412802366921, 57896044618658097711785492504343953925273862865136528165617039157077296866063 (list; graph; refs; listen; history; text; internal format)
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 A167582 A068420

Adjacent sequences:  A246534 A246535 A246536 * A246538 A246539 A246540

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Aug 28 2014

STATUS

approved

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Last modified May 23 20:23 EDT 2019. Contains 323528 sequences. (Running on oeis4.)