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A000107
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Number of rooted trees with n nodes and a single labeled node; pointed rooted trees; vertebrates.
(Formerly M1442 N0570)
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17
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0, 1, 2, 5, 13, 35, 95, 262, 727, 2033, 5714, 16136, 45733, 130046, 370803, 1059838, 3035591, 8710736, 25036934, 72069134, 207727501, 599461094, 1731818878, 5008149658, 14496034714, 41993925955, 121747732406, 353221737526, 1025471857282, 2978995353959, 8658997820084
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 61, 62 (2.1.8-2.1.10)
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134.
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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T. D. Noe, Table of n, a(n) for n=0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 123
N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
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MAPLE
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with (numtheory): b:= proc(n) option remember; `if` (n<2, n, add (add (d*b(d), d=divisors(j)) *b(n-j), j=1..n-1) /(n-1)) end: a:= proc(n) option remember; b(n) +add (a(n-i) *b(i), i=1..n-1) end: seq (a(n), n=0..26); [From Alois P. Heinz, Jun 02 2009]
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MATHEMATICA
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b[0] = 0; b[1] = 1; b[n_] := b[n] = Sum[ Sum[ d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}]/(n-1); a[n_] := a[n] = b[n] + Sum[ a[n-i]*b[i], {i, 1, n-1}]; Table[ a[n], {n, 0, 26}](* From Jean-François Alcover, Mar 07 2012, after Alois P. Heinz *)
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CROSSREFS
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INVERT transform of A000081. Cf. A000243, A000269, A000312, A000444, A000485, A000524-A000526.
Sequence in context: A024576 A057960 A007075 * A063028 A085810 A005773
Adjacent sequences: A000104 A000105 A000106 * A000108 A000109 A000110
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Better description from Christian G. Bower, Apr 15 1998.
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STATUS
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approved
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