1,3

When convolved with itself gives A000151.

Number of rooted trees with n nodes and edges not attached to root are 2-colored or oriented.

Also number of 2-trees (with 2n+1 cells) rooted at a symmetric end-edge. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 22 2001

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.5.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 75, Eq. (3.5.3).

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

Alois P. Heinz, Table of n, a(n) for n = 1..150

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 428

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

a(n+1) is Euler transform of A000151.

G.f.: A(x) = x*exp( A(x)^2/x + A(x^2)^2/(2x^2) + A(x^3)^2/(3x^3) +...+ A(x^n)^2/(n*x^n) +...). - Paul D. Hanna (pauldhanna(AT)juno.com)

A(x) = x + x^2 + 3*x^3 + 10*x^4 + 39*x^5 + 160*x^6 + 702*x^7 +...

A:= proc(n) option remember; if n=0 then 0 else unapply (convert (series (x*exp (add ((A(n-1)(x^k))^2/(k*x^k), k=1..2*n)), x=0, 2*n), polynom), x) fi end: a:= n-> coeff (series ( A(n)(x), x=0, n+1), x, n): seq (a(n), n=1..23); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 20 2008]

Cf. A058870, A058866, A054581.

Sequence in context: A007163 A050385 A123768 this_sequence A151068 A151069 A151070

Adjacent sequences: A005747 A005748 A005749 this_sequence A005751 A005752 A005753

nonn

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

More terms, formula and comment from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.