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A322067
Size of the free distributive lattice on the meet semilattice of partitions.
0
2, 3, 10, 328
OFFSET
1,1
EXAMPLE
n=1: There is one partition of {1}, and the free distributive lattice on this (the unique) one-element meet-semilattice has a(1)=2 elements.
n=2: There are two partitions of {1,2}, and the free distributive lattice on this (the unique) two-element meet-semilattice has a(2)=3 elements.
n=3: There are five partitions of {1,2,3}, and the free distributive lattice on the meet semilattice {123, 12, 23, 13, top) has a(3)=10 elements.
n=4: There are 15 partitions of {1,2,3,4}, and the free distributive lattice on this meet-semilattice has
328 = 1 +
C(6,0) * 2^7 +
C(6,1) * 2^4 +
C(6,2) * 2^2 +
C(6,3) +
C(6,4) +
C(6,5) +
C(6,6) +
1
elements, where the C(n,k) are binomial coefficients.
CROSSREFS
Sequence in context: A364140 A358391 A132536 * A302250 A290638 A330294
KEYWORD
nonn,more
AUTHOR
David Spivak, Nov 25 2018
STATUS
approved