A327697 Number of refinement sequences n -> ... -> {1}^n, where in each step every single part of a nonempty selection of parts is replaced by a partition of itself into smaller parts (in weakly decreasing order).

1, 1, 2, 7, 22, 122, 598, 4683, 31148, 292008, 2560274, 30122014, 313694962, 4189079688, 53048837390, 826150653479, 11827659365138, 204993767192252, 3371451881544534, 65337695492942258, 1198123466804343518, 25318312971995895392, 516420623159289735874

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Wikipedia, Partition (number theory)

Example

a(1) = 1:
  1
a(2) = 1:
  2 -> 11
a(3) = 2:
  3 -> 111
  3 -> 21   -> 111
a(4) = 7:
  4 -> 1111
  4 -> 211  -> 1111
  4 -> 31   -> 1111
  4 -> 31   -> 211  -> 1111
  4 -> 22   -> 1111
  4 -> 22   -> 112  -> 1111
  4 -> 22   -> 211  -> 1111

Crossrefs

Cf. A002846, A327643, A327698, A327699, A327702.

Sequence in context: A217138 A004300 A049369 * A308548 A153523 A153551

Adjacent sequences: A327694 A327695 A327696 * A327698 A327699 A327700

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2019

Status

approved