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%I #10 Apr 08 2018 20:10:02
%S 1,3,14,85,586,4331,33545,268521,2204249
%N Number of positive subset-sum trees of weight n.
%C A positive subset-sum tree with root x is either the symbol x itself, or is obtained by first choosing a positive subset-sum x <= (y_1,...,y_k) with k > 1 and then choosing a positive subset-sum tree with root y_i for each i = 1...k. The weight is the sum of the leaves. We write positive subset-sum trees in the form rootsum(branch,...,branch). For example, 4(1(1,3),2,2(1,1)) is a positive subset-sum tree with composite 4(1,1,1,2,3) and weight 8.
%e The a(3) = 14 positive subset-sum trees:
%e 3 3(1,2) 3(1,1,1) 3(1,2(1,1))
%e 2(1,2) 2(1,1,1) 2(1,1(1,1)) 2(1(1,1),1) 2(1,2(1,1))
%e 1(1,2) 1(1,1,1) 1(1,1(1,1)) 1(1(1,1),1) 1(1,2(1,1))
%Y Cf. A000108, A000712, A108917, A122768, A262671, A262673, A275972, A276024, A284640, A299701, A301854, A301855, A301856, A301935.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Mar 28 2018
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