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

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

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: A018826 A342130 A258624 * A280783 A104899 A057975

Adjacent sequences: A236289 A236290 A236291 * A236293 A236294 A236295

Keyword

nonn,easy

Author

Clark Kimberling, Jan 22 2014

Status

approved