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 A331578 Number of labeled series-reduced rooted trees with n vertices and more than two branches of the root. 6
 0, 0, 0, 4, 5, 186, 847, 17928 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A rooted tree is series-reduced if no vertex (including the root) has degree 2. Also labeled lone-child-avoiding rooted trees with n vertices and more than two branches, where a rooted tree is lone-child-avoiding if no vertex has exactly one child. LINKS EXAMPLE Non-isomorphic representatives of the a(7) = 847 trees (in the format root[branches]) are:   1[2,3,4[5,6,7]]   1[2,3,4,5[6,7]]   1[2,3,4,5,6,7] MATHEMATICA lrt[set_]:=If[Length[set]==0, {}, Join@@Table[Apply[root, #]&/@Join@@Table[Tuples[lrt/@stn], {stn, sps[DeleteCases[set, root]]}], {root, set}]]; Table[Length[Select[lrt[Range[n]], Length[#]>2&&FreeQ[#, _[_]]&]], {n, 6}] CROSSREFS The non-series-reduced version is A331577. The unlabeled version is A331488. Lone-child-avoiding rooted trees are counted by A001678. Topologically series-reduced rooted trees are counted by A001679. Labeled topologically series-reduced rooted trees are counted by A060313. Labeled lone-child-avoiding rooted trees are counted by A060356. Matula-Goebel numbers of lone-child-avoiding rooted trees are A291636. Matula-Goebel numbers of series-reduced rooted trees are A331489. Cf. A000014, A000169, A000669, A005512, A108919, A206429, A331233, A331490. Sequence in context: A270551 A041409 A101076 * A041745 A298224 A051152 Adjacent sequences:  A331575 A331576 A331577 * A331579 A331580 A331581 KEYWORD nonn,more AUTHOR Gus Wiseman, Jan 21 2020 STATUS approved

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Last modified September 29 10:54 EDT 2020. Contains 337428 sequences. (Running on oeis4.)