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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 September 8 08:26 EDT 2024. Contains 375753 sequences. (Running on oeis4.)