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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).

%I A327702 #12 Sep 23 2019 17:25:33
%S A327702 1,1,2,5,14,47,174,730,3300,16361,85991,485982,2877194,18064663,
%T A327702 118111993,810388956,5755059363,42643884970,325468477721,
%U A327702 2576976440845,20960795772211,176056148076418,1514733658531058,13418942409623726,121442280888373117,1128425823360525506
%N 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).
%H A327702 Alois P. Heinz, <a href="/A327702/b327702.txt">Table of n, a(n) for n = 1..58</a>
%H A327702 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%e A327702 a(4) = 5:
%e A327702   4 -> 1111
%e A327702   4 -> 211  -> 1111
%e A327702   4 -> 31   -> 1111
%e A327702   4 -> 31   -> 211  -> 1111
%e A327702   4 -> 22   -> 211  -> 1111
%p A327702 v:= l-> [seq(`if`(i=1 or l[i]>l[i-1], seq(subs(1=[][], sort(
%p A327702          subsop(i=h[], l))), h=({combinat[partition](l[i])[]}
%p A327702          minus{[l[i]]})), [][]), i=1..nops(l))]:
%p A327702 b:= proc(l) option remember; `if`(max(l)<2, 1, add(b(h), h=v(l))) end:
%p A327702 a:= n-> b([n]):
%p A327702 seq(a(n), n=1..26);
%Y A327702 Cf. A002846, A327643, A327697, A327698, A327699.
%K A327702 nonn
%O A327702 1,3
%A A327702 _Alois P. Heinz_, Sep 22 2019