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A114572
Number of "ultrasweet" Boolean functions of n variables which depend on all the variables.
4
2, 1, 2, 6, 27, 185, 2135, 55129
OFFSET
0,1
COMMENTS
Inverse binomial transform of A114491.
This sequence enumerates a certain type of matroid, except for the first entry (which is 2 instead of 1). If the first entry is changed from 2 to 1, giving A118085, this enumerates "combinatorial geometries" on n labeled points.
These are matroids in which no element has rank 0; equivalently, all one-element sets are independent; equivalently, the closure of the empty set is empty.
These are called "simple matroids" in A002773. So A118085 is the "labeled" equivalent of that sequence, which counts unlabeled points.
EXAMPLE
For all n>1, a function like "x2" is counted in A114491 but not in the present sequence.
CROSSREFS
KEYWORD
nonn
AUTHOR
Don Knuth, Aug 17 2008, Oct 14 2008
STATUS
approved