A327698 Number of refinement sequences n -> ... -> {1}^n, where in each step exactly one part is replaced by a partition of itself into smaller parts (in weakly decreasing order).

1, 1, 2, 6, 17, 74, 300, 1755, 9360, 65510, 442117, 3802889, 30213386, 294892947, 2789021105, 31360525517, 334374848070, 4184958056248, 50606351991305, 704124800141153, 9452367941048830, 143309007303310536, 2124982437997726705, 35389562541842450218

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Wikipedia, Partition (number theory)

Example

a(4) = 6:
  4 -> 1111
  4 -> 211  -> 1111
  4 -> 31   -> 1111
  4 -> 31   -> 211  -> 1111
  4 -> 22   -> 112  -> 1111
  4 -> 22   -> 211  -> 1111

Crossrefs

Cf. A002846, A327643, A327697, A327699, A327702.

Sequence in context: A079456 A264761 A253882 * A183757 A356011 A181490

Adjacent sequences: A327695 A327696 A327697 * A327699 A327700 A327701

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2019

Status

approved