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 A236292 Number of distinct cyclic permutations of the partitions of n; see comments. 2
 1, 2, 4, 8, 16, 27, 48, 75, 118, 178, 265, 377, 544, 760, 1048, 1437, 1949, 2611, 3480, 4594, 6024, 7867, 10184, 13122, 16823, 21484, 27258, 34495, 43425, 54499, 68105, 84870, 105322, 130412, 160832, 197932, 242776, 297145, 362535, 441464, 536064, 649703 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..400 FORMULA 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. EXAMPLE 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). MATHEMATICA Map[Total[Map[Length, Map[(# /. Table[x_, {Length[#]}] -> {x}) &,     IntegerPartitions[#]]]] &, Range[40]] (* A236292 *) (* Peter J. C. Moses, Jan 21 2014 *) CROSSREFS Cf. A236293. Sequence in context: A322326 A018826 A258624 * A280783 A104899 A057975 Adjacent sequences:  A236289 A236290 A236291 * A236293 A236294 A236295 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jan 22 2014 STATUS approved

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Last modified December 12 05:15 EST 2018. Contains 318052 sequences. (Running on oeis4.)