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A236292 Number of distinct cyclic permutations of the partitions of n; see comments.

%I A236292 #10 Feb 06 2014 09:54:39
%S A236292 1,2,4,8,16,27,48,75,118,178,265,377,544,760,1048,1437,1949,2611,3480,
%T A236292 4594,6024,7867,10184,13122,16823,21484,27258,34495,43425,54499,68105,
%U A236292 84870,105322,130412,160832,197932,242776,297145,362535,441464,536064,649703
%N A236292 Number of distinct cyclic permutations of the partitions of n; see comments.
%C A236292 Suppose that p = [x(1),...,x(k)], is a partition of n, where x(1) <= x(2) <= ... <= x(k).  If x(1) = x(k), there is only one cyclic permutation of p; otherwise, there are k of them.
%H A236292 Alois P. Heinz, <a href="/A236292/b236292.txt">Table of n, a(n) for n = 1..400</a>
%F A236292 a(n) = (d(n), f(2), f(3),..., f(n-1))*(1,2,3,...,n-1), where d(n) = (number of divisors of n) = (number of constant partitions of n), and f(k) = number of nonconstant partitions of n, for k = 2,3,...,n-1.
%e A236292 a(6) = (4,2,2,2,1)*(1,2,3,4,5) = 27, where * = convolution.  The 5 components of (4,2,2,2,1) count these partitions:  (6, 33, 222, 1111);  (51, 42); (411, 321); (3111, 2211);  (211111).
%t A236292 Map[Total[Map[Length, Map[(# /. Table[x_, {Length[#]}] -> {x}) &,     IntegerPartitions[#]]]] &, Range[40]] (* A236292 *)
%t A236292 (* _Peter J. C. Moses_, Jan 21 2014 *)
%Y A236292 Cf. A236293.
%K A236292 nonn,easy
%O A236292 1,2
%A A236292 _Clark Kimberling_, Jan 22 2014