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A358581
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Number of rooted trees with n nodes, most of which are leaves.
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17
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1, 0, 1, 1, 4, 5, 20, 28, 110, 169, 663, 1078, 4217, 7169, 27979, 49191, 191440, 345771, 1341974, 2477719, 9589567, 18034670, 69612556, 132984290, 511987473, 991391707, 3807503552, 7460270591, 28585315026, 56595367747, 216381073935, 432396092153
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OFFSET
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1,5
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(7) = 20 trees:
o . (oo) (ooo) (oooo) (ooooo) (oooooo)
((ooo)) ((oooo)) ((ooooo))
(o(oo)) (o(ooo)) (o(oooo))
(oo(o)) (oo(oo)) (oo(ooo))
(ooo(o)) (ooo(oo))
(oooo(o))
(((oooo)))
((o)(ooo))
((o(ooo)))
((oo)(oo))
((oo(oo)))
((ooo(o)))
(o((ooo)))
(o(o)(oo))
(o(o(oo)))
(o(oo(o)))
(oo((oo)))
(oo(o)(o))
(oo(o(o)))
(ooo((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[#, {}, {0, Infinity}]>Count[#, _[__], {0, Infinity}]&]], {n, 0, 10}]
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PROG
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seq(n) = {my(A=R(n)); vector(n, n, my(u=Vecrev(A[n]/y)); vecsum(u[n\2+1..#u]))} \\ Andrew Howroyd, Dec 31 2022
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CROSSREFS
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A358575 counts rooted trees by nodes and internal nodes, ordered A090181.
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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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