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%I A114572
%S A114572 2,1,2,6,27,185,2135,55129
%N A114572 Number of "ultrasweet" Boolean functions of n variables which depend 
               on all the variables.
%C A114572 Inverse binomial transform of A114491.
%C A114572 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 A114572 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 A114572 These are called "simple matroids" in A002773. So A118085 is the "labeled" 
               equivalent of that sequence, which counts unlabeled points.
%e A114572 For all n>1, a function like "x2" is counted in A114491 but not in the 
               present sequence.
%Y A114572 Cf. A114302, A114303, A114491, A118085, A002773.
%Y A114572 Sequence in context: A032163 A038078 A000139 this_sequence A052621 A131057 
               A051852
%Y A114572 Adjacent sequences: A114569 A114570 A114571 this_sequence A114573 A114574 
               A114575
%K A114572 nonn
%O A114572 0,1
%A A114572 D. E. Knuth, Aug 17 2008, Oct 14 2008

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