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A358723
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Number of n-node rooted trees of edge-height equal to their number of leaves.
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1
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0, 1, 0, 2, 1, 6, 7, 26, 43, 135, 276, 755, 1769, 4648, 11406, 29762, 75284, 195566, 503165, 1310705, 3402317, 8892807, 23231037, 60906456, 159786040, 420144405, 1105673058, 2914252306, 7688019511, 20304253421, 53667498236, 141976081288, 375858854594, 995728192169
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OFFSET
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1,4
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COMMENTS
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Edge-height (A109082) is the number of edges in the longest path from root to leaf.
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LINKS
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EXAMPLE
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The a(1) = 0 through a(7) = 7 trees:
. (o) . ((oo)) ((o)(o)) (((ooo))) (((o))(oo))
(o(o)) ((o(oo))) (((o)(oo)))
((oo(o))) ((o)((oo)))
(o((oo))) ((o)(o(o)))
(o(o(o))) ((o(o)(o)))
(oo((o))) (o((o)(o)))
(o(o)((o)))
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MATHEMATICA
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art[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[art/@c], OrderedQ], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[Select[art[n], Count[#, {}, {-2}]==Depth[#]-2&]], {n, 1, 10}]
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PROG
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(PARI) \\ Needs R(n, f) defined in A358589.
seq(n) = {Vec(R(n, (h, p)->polcoef(p, h-1, y)), -n)} \\ Andrew Howroyd, Jan 01 2023
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CROSSREFS
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For internals instead of edge-height: A185650 aerated, ranked by A358578.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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