[seqfan] G.f. for trees with degree at most 3

franktaw at netscape.net franktaw at netscape.net
Sun May 23 23:51:17 CEST 2010

I asked the author of this sequence for clarification, but got no
response. Maybe somebody here can figure out what is going on.

http://www.research.att.com/~njas/sequences/A003692

For this sequence, a generating function is given:

(1-x)(2-x-x^2) - (2-x+x^2)\sqrt{1-2x-x^2} \over 3 x^3.

I'm not sure if this is supposed to be

(1-x)*(2-x-x^2)-(2-x-x^2)*sqrt(1-2*x-x^2)/(3*x^3)

or

((1-x)*(2-x-x^2)-(2-x-x^2)*sqrt(1-2*x-x^2))/(3*x^3),

but either one produces a series that includes terms with negative
exponents; and in neither case there is any apparent relationship to
this sequence. So what is the correct g.f.?