A118077 Number of edges in the representation of all linear extensions of the inclusion ordering on P({1,...,n}) as distributive lattice contained in P(P({1,...,n})).

1, 2, 6, 32, 454, 35512, 66584412, 36566354210304

Offset

0,2

Comments

The numbers of vertices are the Dedekind numbers (A000372) and A046873 is the total number of linear extensions.

Links

Table of n, a(n) for n=0..7.

Formula

a(n) = Sum_{m=1..C(n,floor(n/2))} A059119(n,m)*m. - Geoffrey Critzer, Aug 11 2020

Example

a(2) = 6 as the lattice is { {}, { {} }, { {}, {1} }, { {}, {2} }, { {}, {1}, {2}}, { {}, {1}, {2}, {1, 2} } }.

Crossrefs

Cf. A046873, A000372, A059119.

Sequence in context: A067735 A326901 A332537 * A013976 A213435 A372902

Adjacent sequences: A118074 A118075 A118076 * A118078 A118079 A118080

Keyword

nonn,hard,more

Author

Oliver Wienand, Apr 11 2006

Extensions

a(7) added by Geoffrey Critzer, Aug 11 2020 from A059119

a(7) corrected by Lennart Van Hirtum, Apr 02 2025

Status

approved