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A358582
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Number of rooted trees with n nodes, most of which are not leaves.
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9
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0, 0, 1, 1, 5, 7, 28, 48, 176, 336, 1179, 2420, 8269, 17855, 59832, 134289, 443407, 1025685, 3346702, 7933161, 25632265, 62000170, 198670299, 488801159, 1555187172, 3882403641, 12276230777, 31034921462, 97601239282, 249471619165, 780790439063, 2015194486878
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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(3) = 1 through a(6) = 7 trees:
((o)) (((o))) (((oo))) ((((oo))))
((o)(o)) (((o)(o)))
((o(o))) (((o(o))))
(o((o))) ((o)((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[#, {}, {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, vecsum(Vecrev(A[n]/y)[1..(n-1)\2]))} \\ Andrew Howroyd, Dec 30 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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