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%I #4 Aug 08 2015 23:57:49
%S 2,1,2,6,27,185,2135,55129
%N Number of "ultrasweet" Boolean functions of n variables which depend on all the variables.
%C Inverse binomial transform of A114491.
%C 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.
%C 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.
%C These are called "simple matroids" in A002773. So A118085 is the "labeled" equivalent of that sequence, which counts unlabeled points.
%e For all n>1, a function like "x2" is counted in A114491 but not in the present sequence.
%Y Cf. A114302, A114303, A114491, A118085, A002773.
%K nonn
%O 0,1
%A _Don Knuth_, Aug 17 2008, Oct 14 2008
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