cp's OEIS Frontend

A327697 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).

%I A327697 #12 Sep 23 2019 17:27:16
%S A327697 1,1,2,7,22,122,598,4683,31148,292008,2560274,30122014,313694962,
%T A327697 4189079688,53048837390,826150653479,11827659365138,204993767192252,
%U A327697 3371451881544534,65337695492942258,1198123466804343518,25318312971995895392,516420623159289735874
%N A327697 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 A327697 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%e A327697 a(1) = 1:
%e A327697   1
%e A327697 a(2) = 1:
%e A327697   2 -> 11
%e A327697 a(3) = 2:
%e A327697   3 -> 111
%e A327697   3 -> 21   -> 111
%e A327697 a(4) = 7:
%e A327697   4 -> 1111
%e A327697   4 -> 211  -> 1111
%e A327697   4 -> 31   -> 1111
%e A327697   4 -> 31   -> 211  -> 1111
%e A327697   4 -> 22   -> 1111
%e A327697   4 -> 22   -> 112  -> 1111
%e A327697   4 -> 22   -> 211  -> 1111
%Y A327697 Cf. A002846, A327643, A327698, A327699, A327702.
%K A327697 nonn
%O A327697 1,3
%A A327697 _Alois P. Heinz_, Sep 22 2019