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A000238 Number of oriented trees with n nodes.
(Formerly M2756 N1108)
6
1, 1, 3, 8, 27, 91, 350, 1376, 5743, 24635, 108968, 492180, 2266502, 10598452, 50235931, 240872654, 1166732814, 5702001435, 28088787314, 139354922608, 695808554300, 3494390057212, 17641695461662, 89495023510876, 456009893224285, 2332997330210440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 286.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 60, r(x).

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 138.

R. Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1991), 93-104.

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).

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..350

Index entries for sequences related to trees

FORMULA

G.f. = x+x^2+3*x^3+8*x^4+27*x^5+... = R(x)-R(x)^2, where R(x) = g.f. for A000151.

MAPLE

A:= proc(n) option remember; if n=0 then 0 else unapply (convert (series (x*exp (2* add (A(n-1)(x^k)/k, k=1..n-1)), x=0, n), polynom), x) fi end: a:= n-> coeff (series (A(n+1)(x) *(1-A(n+1)(x)), x=0, n+1), x, n): seq (a(n), n=1..26); # Alois P. Heinz, Aug 20 2008

MATHEMATICA

A[n_][y_] := A[n][y] = If[n == 0, 0, Normal[Series[x*Exp[2*Sum[A[n-1][x^k]/k, {k, 1, n-1}]], {x, 0, n}] /. x -> y]]; a[n_] := SeriesCoefficient[A[n+1][x]*(1-A[n+1][x]), {x, 0, n}]; Table[a[n], {n, 1, 26}] (* Jean-Fran├žois Alcover, Feb 12 2014, translated from Maple *)

CROSSREFS

Sequence in context: A148839 A148840 A047153 * A148841 A148842 A148843

Adjacent sequences:  A000235 A000236 A000237 * A000239 A000240 A000241

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

2 errors corrected by Paul Zimmermann, Mar 01, 1996

More terms from N. J. A. Sloane, Mar 10 2007

STATUS

approved

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Last modified July 25 19:05 EDT 2014. Contains 244918 sequences.