A327702 Number of refinement sequences n -> ... -> {1}^n, where in each step one part that is the rightmost copy of its size is replaced by a partition of itself into smaller parts (in weakly decreasing order).

1, 1, 2, 5, 14, 47, 174, 730, 3300, 16361, 85991, 485982, 2877194, 18064663, 118111993, 810388956, 5755059363, 42643884970, 325468477721, 2576976440845, 20960795772211, 176056148076418, 1514733658531058, 13418942409623726, 121442280888373117, 1128425823360525506

Offset: 1

Author

Alois P. Heinz, Sep 22 2019

Keywords

• nonn

Examples

			a(4) = 5:
  4 -> 1111
  4 -> 211  -> 1111
  4 -> 31   -> 1111
  4 -> 31   -> 211  -> 1111
  4 -> 22   -> 211  -> 1111
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..58
• Wikipedia, Partition (number theory)

Crossrefs

Cf. A002846, A327643, A327697, A327698, A327699.

Programs

Maple

v:= l-> [seq(`if`(i=1 or l[i]>l[i-1], seq(subs(1=[][], sort(
         subsop(i=h[], l))), h=({combinat[partition](l[i])[]}
         minus{[l[i]]})), [][]), i=1..nops(l))]:
b:= proc(l) option remember; `if`(max(l)<2, 1, add(b(h), h=v(l))) end:
a:= n-> b([n]):
seq(a(n), n=1..26);