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A032027
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Number of planted planar trees (n+1 nodes) where any 2 subtrees extending from the same node are different.
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16
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1, 1, 1, 3, 5, 13, 35, 95, 255, 715, 2081, 6003, 17645, 52127, 155863, 468129, 1415521, 4301055, 13134789, 40275109, 123970669, 382919917, 1186475687, 3686899725, 11487023793, 35876838669, 112304155021, 352276801491
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OFFSET
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1,4
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LINKS
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FORMULA
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Shifts left under "AGK" (ordered, elements, unlabeled) transform.
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EXAMPLE
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The a(1) = 1 through a(6) = 13 ordered rooted identity trees (ranked by A358374):
o (o) ((o)) ((o)o) (((o))o) (((o)o)o)
(o(o)) (((o)o)) ((o(o))o)
(((o))) ((o(o))) (o((o)o))
(o((o))) (o(o(o)))
((((o)))) ((((o)))o)
((((o))o))
((((o)o)))
(((o))(o))
(((o(o))))
((o)((o)))
((o((o))))
(o(((o))))
(((((o)))))
(End)
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MATHEMATICA
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aot[n_]:=If[n==1, {{}}, Join@@Table[Tuples[aot/@c], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[aot[n], FreeQ[#, _[__]?(!UnsameQ@@#&)]&]], {n, 1, 10}] (* Gus Wiseman, Nov 15 2022 *)
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PROG
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(PARI)
AGK(v)={apply(p->subst(serlaplace(y^0*p), y, 1), Vec(prod(k=1, #v, (1 + x^k*y + O(x*x^#v))^v[k])-1, -#v))}
seq(n)={my(v=[1]); for(i=2, n, v=concat([1], AGK(v))); v} \\ Andrew Howroyd, Sep 20 2018
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CROSSREFS
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These trees (ordered rooted identity) are ranked by A358374.
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KEYWORD
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nonn,eigen
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AUTHOR
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STATUS
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approved
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