0,7

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 284.

D. G. Cantor, personal communication.

F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969, p. 232.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 62, Fig. 3.3.3.

F. Harary and G. Prins, The number of homeomorphically irreducible trees and other species, Acta Math., 101 (1959), 141-162.

F. Harary, R. W. Robinson and A. J. Schwenk, Twenty-step algorithm for determining the asymptotic number of trees of various species, J. Austral. Math. Soc., Series A, 20 (1975), 483-503. Errata: Vol. A 41 (1986), p. 325.

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 526.

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).

Christian G. Bower, Table of n, a(n) for n = 0..500

N. J. A. Sloane, Illustration of initial terms

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for sequences related to trees

Index entries for "core" sequences

G.f.: A(x) = ((x-1)/x)*f(x) + ((1+x)/x^2)*g(x) - (1/x^2)*g(x)^2 where f(x) is g.f. for A059123 and 1+g(x) is g.f. for A001678. [Harary and E. M. Palmer, p. 62, Eq. (3.3.10) with extra -(1/x^2)*Hbar(x)^2 term which should be there according to eq.(3.3.14), p. 63, with eq.(3.3.9)].

with (powseries): with (combstruct): n := 30: Order := n+3: sys := {B = Prod(C, Z), S = Set(B, 1 <= card), C = Union(Z, S)}:

G001678 := (convert(gfseries(sys, unlabeled, x) [S(x)], polynom)) * x^2: G0temp := G001678 + x^2:

G059123 := G0temp / x + G0temp - (G0temp^2+eval(G0temp, x=x^2))/(2*x):

G000014 := ((x-1)/x) * G059123 + ((1+x)/x^2) * G0temp - (1/x^2) * G0temp^2:

A000014 := 0, seq(coeff(G000014, x^i), i=1..n); # from UlrSchimke(AT)aol.com

Cf. A000055 (trees), A001678 (series-reduced planted trees), A007827 (series-reduced trees by leaves).

Sequence in context: A147678 A127712 A032090 this_sequence A114851 A099364 A125951

Adjacent sequences: A000011 A000012 A000013 this_sequence A000015 A000016 A000017

nonn,easy,core,nice

N. J. A. Sloane (njas(AT)research.att.com).

G.f. corrected by Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 09 2001.