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A001854
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Total height of all rooted trees on n labeled nodes
(Formerly M2081 N0822)
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7
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0, 2, 15, 148, 1785, 26106, 449701, 8927192, 200847681, 5053782070, 140679853941, 4293235236324, 142553671807729, 5116962926162738, 197459475792232725, 8152354312656732976, 358585728464893234305, 16741214317684425260142, 826842457727306803110997, 43073414675338753123113980
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OFFSET
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1,2
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COMMENTS
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Take any one of the n^(n-1) rooted trees on n labeled nodes, compute its height (maximal edge distance to root), sum over all trees.
a(n) = Sum_{k=1..n-1} A034855(n,k)*k. - Geoffrey Critzer, Mar 14 2013
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REFERENCES
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J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..100
Index entries for sequences related to trees
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MATHEMATICA
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nn=20; a=NestList[ x Exp[#]&, x, nn]; f[list_]:=Sum[list[[i]]*i, {i, 1, Length[list]}]; Drop[Map[f, Transpose[Table[Range[0, nn]!CoefficientList[Series[a[[i+1]]-a[[i]], {x, 0, nn}], x], {i, 1, nn-1}]]], 1] (* Geoffrey Critzer, Mar 14 2013 *)
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CROSSREFS
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Cf. A034855, A236396. A234953(n) = a(n)/n.
Sequence in context: A224885 A253571 A111686 * A060226 A002103 A191364
Adjacent sequences: A001851 A001852 A001853 * A001855 A001856 A001857
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Geoffrey Critzer, Mar 14 2013
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STATUS
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approved
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