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A300352
Number of strict trees of weight n with distinct leaves.
9
1, 1, 2, 2, 3, 6, 8, 11, 17, 40, 48, 76, 109, 159, 400, 470, 745, 1057, 1576, 2103, 5267, 6022, 9746, 13390, 20099, 26542, 39396, 82074, 101387, 152291, 215676, 308937, 423587, 596511, 799022, 1623311, 1960223, 2947722, 4048704, 5845982, 7794809, 11028888
OFFSET
1,3
COMMENTS
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.
FORMULA
a(n) = Sum_{i=1..A000009(n)} A294018(A246867(n,i)).
EXAMPLE
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).
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=
Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
str[q_]:=str[q]=If[Length[q]===1, 1, Total[Times@@@Map[str, Select[sps[q], And[Length[#]>1, UnsameQ@@Total/@#]&], {2}]]];
Table[Total[str/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 1, 20}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 03 2018
STATUS
approved