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%I #12 Sep 23 2019 17:27:16
%S 1,1,2,7,22,122,598,4683,31148,292008,2560274,30122014,313694962,
%T 4189079688,53048837390,826150653479,11827659365138,204993767192252,
%U 3371451881544534,65337695492942258,1198123466804343518,25318312971995895392,516420623159289735874
%N 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).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%e a(1) = 1:
%e 1
%e a(2) = 1:
%e 2 -> 11
%e a(3) = 2:
%e 3 -> 111
%e 3 -> 21 -> 111
%e a(4) = 7:
%e 4 -> 1111
%e 4 -> 211 -> 1111
%e 4 -> 31 -> 1111
%e 4 -> 31 -> 211 -> 1111
%e 4 -> 22 -> 1111
%e 4 -> 22 -> 112 -> 1111
%e 4 -> 22 -> 211 -> 1111
%Y Cf. A002846, A327643, A327698, A327699, A327702.
%K nonn
%O 1,3
%A _Alois P. Heinz_, Sep 22 2019
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