

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
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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(n1))*(1,2,3,...,n1), 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,...,n1.


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



