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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 06:48 EDT 2019. Contains 322209 sequences. (Running on oeis4.)