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A198254 Number of maximum-diversity partitions of n.

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%I A198254 #10 Apr 16 2015 07:13:01
%S A198254 1,1,2,1,1,1,2,1,1,2,1,1,1,1,1,2,1,3,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,
%T A198254 1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,
%U A198254 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A198254 Number of maximum-diversity partitions of n.
%C A198254 A maximum-diversity partition of n is an integer partition whose part distribution maximizes the number of different compositions (=distinct partition orderings) that can be constructed from it.
%C A198254 An integer composition of n corresponds to a subgroup of the symmetric group on n element whose cycles are formed of contiguous integers.
%H A198254 Alois P. Heinz, <a href="/A198254/b198254.txt">Table of n, a(n) for n = 0..1000</a>
%e A198254 For n=17, there are 3 partitions reaching the maximum possible of 7!/2 =2520 distinct orderings : {4, 3, 2, 2, 2, 1, 1, 1, 1}, {4, 3, 2, 2, 1, 1, 1, 1, 1, 1} and {3, 3, 2, 2, 2, 1, 1, 1, 1, 1}.
%Y A198254 A102462 gives the number of compositions that can be constructed from a maximum-diversity partition of n.
%Y A198254 Cf. A007294, A072811, A080575.
%K A198254 nonn,nice
%O A198254 0,3
%A A198254 _Olivier Gérard_, Oct 22 2011