OFFSET
1,3
COMMENTS
There may be an error in eq (37) in the Harary-Robinson paper. - R. J. Mathar, Sep 28 2011
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..80
F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335.
F. Harary and R. W. Robinson, The number of achiral trees, J. Reine Angew. Math., 278 (1975), 322-335. (Annotated scanned copy)
MAPLE
L := BFILETOLIST("b003238.txt") ;
Pofxn := proc(n)
global L;
add( op(i, L)*x^(i+1), i=1..120) ;
subs(x=x^n, %) ;
end proc:
P := Pofxn(1) ;
Rn := proc(n)
global L;
(Pofxn(n-2)*Pofxn(2)+Pofxn(n-1)*Pofxn(1)-Pofxn(n))/x^(n-1) ;
end proc:
Px2 := Pofxn(2) ;
Px3 := Pofxn(3) ;
Px4 := Pofxn(4) ;
# eq (37) seems not to work
# R := 2*x+P^2/x^2+(1-x)*P/x*(Px2/x^2-1)-(P^2-Px2)/2/x -Px3/x^2-(Px2^2-Px4)/2/x^3 ;
#use eqs (39)-(44) instead
R := x+P+(P^2+Px2)/2/x+P*Px2/x^2+P*Px3/x^3+(Px2^2-Px4)/2/x^3 :
# heuristics, adding up to R^(40) suffices for first 80 terms
for n from 5 to 40 do
R := R+Rn(n) :
end do:
taylor(R, x=0, 80) ;
gfun[seriestolist](%) ; # R. J. Mathar, Sep 28 2011
MATHEMATICA
L = Cases[Import["https://oeis.org/A003238/b003238.txt", "Table"], {_, _}][[All, 2]];
Pofxn[n_] := Sum[x^(i+1) L[[i]], {i, 1, 120}] /. x -> x^n;
P = Pofxn[1];
Rn[n_] := (1/x^(n-1))(Pofxn[2] Pofxn[n-2] + Pofxn[1] Pofxn[n-1] - Pofxn[n]);
Px2 = Pofxn[2]; Px3 = Pofxn[3]; Px4 = Pofxn[4];
R = (P^2 + Px2)/(2x) + (P Px2)/x^2 + (P Px3)/x^3 + P + (Px2^2 - Px4)/(2x^3) + x;
For[n = 5, n <= 40, n++, R += Rn[n]];
CoefficientList[R + O[x]^41, x] // Rest (* Jean-François Alcover, Apr 06 2020, from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Extended by R. J. Mathar, Sep 28 2011
STATUS
approved