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

Author

Alois P. Heinz, Sep 22 2019

Keywords

• nonn

Examples

			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
		

Links

• Wikipedia, Partition (number theory)

Crossrefs

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