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%I #11 Sep 23 2019 17:27:49
%S 1,1,2,6,17,74,300,1755,9360,65510,442117,3802889,30213386,294892947,
%T 2789021105,31360525517,334374848070,4184958056248,50606351991305,
%U 704124800141153,9452367941048830,143309007303310536,2124982437997726705,35389562541842450218
%N 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).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%e a(4) = 6:
%e 4 -> 1111
%e 4 -> 211 -> 1111
%e 4 -> 31 -> 1111
%e 4 -> 31 -> 211 -> 1111
%e 4 -> 22 -> 112 -> 1111
%e 4 -> 22 -> 211 -> 1111
%Y Cf. A002846, A327643, A327697, A327699, A327702.
%K nonn
%O 1,3
%A _Alois P. Heinz_, Sep 22 2019