1,2

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.

N. J. A. Sloane, Table of n, a(n) for n = 1..500

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 387

P. Leroux and B. Miloudi, Generalisations de la formule d'Otter, Ann. Sci. Math. Quebec 16 (1992), no 1, 53-80.

S. G. Wagner, An identity for the cycle indices of rooted tree automorphism groups, Elec. J. Combinat., 13 (2006), #R00.

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

a(n+1) has g.f.: prod from n=1 to inf (1 - x^(2*a(n)))^(-1). [This doesn't seem to make sense! - njas]

Generating function A(x) = x+2*x^2+7*x^3+26*x^4+... satisfies A(x)=x*exp( 2*sum_{k>=1}(A(x^k)/k) ) [Harary]. - Pab Ter (pabrlos2(AT)yahoo.com), Oct 12 2005

R:=series(x+2*x^2+7*x^3+26*x^4, x, 5); M:=500;

for n from 5 to M do

series(add( subs(x=x^k, R)/k, k=1..n-1), x, n);

t4:=coeff(series(x*exp(%)^2, x, n+1), x, n);

R:=series(R+t4*x^n, x, n+1); od:

for n from 1 to M do lprint(n, coeff(R, x, n)); od: - njas, Mar 10 2007

with(combstruct):norootree:=[S, {B = Set(S), S = Prod(Z, B, B)}, unlabeled] :seq(count(norootree, size=i), i=1..30); # with Algolib (Pab Ter)

Cf. A000238, A038055.

Also the self-convolution of A005750. - Paul D. Hanna (pauldhanna(AT)juno.com), Aug 17 2002

Adjacent sequences: A000148 A000149 A000150 this_sequence A000152 A000153 A000154

Sequence in context: A141370 A052706 A122871 this_sequence A102319 A006603 A080244

nonn,easy,eigen,nice

njas

Extended with alternate description by Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 12 2005