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%I #9 Mar 03 2018 22:51:35
%S 1,1,2,2,3,6,8,11,17,40,48,76,109,159,400,470,745,1057,1576,2103,5267,
%T 6022,9746,13390,20099,26542,39396,82074,101387,152291,215676,308937,
%U 423587,596511,799022,1623311,1960223,2947722,4048704,5845982,7794809,11028888
%N Number of strict trees of weight n with distinct leaves.
%C A strict tree of weight n > 0 is either a single node of weight n, or a sequence of two or more strict trees with strictly decreasing weights summing to n.
%F a(n) = Sum_{i=1..A000009(n)} A294018(A246867(n,i)).
%e The a(8) = 11 strict trees with distinct leaves: 8, (71), ((52)1), ((43)1), (62), ((51)2), (53), ((41)3), (5(21)), (521), (431).
%t sps[{}]:={{}};sps[set:{i_,___}]:=
%t Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t str[q_]:=str[q]=If[Length[q]===1,1,Total[Times@@@Map[str,Select[sps[q],And[Length[#]>1,UnsameQ@@Total/@#]&],{2}]]];
%t Table[Total[str/@Select[IntegerPartitions[n],UnsameQ@@#&]],{n,1,20}]
%Y Cf. A000009, A056239, A063834, A196545, A246867, A273873, A281145, A289501, A294018, A294079, A296150, A299201, A299202, A299203, A300353, A300354, A300355.
%K nonn
%O 1,3
%A _Gus Wiseman_, Mar 03 2018
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