

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^k1).
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}}. 163=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^k1));


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



