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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: A060957 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 April 25 00:46 EDT 2017. Contains 285346 sequences.