[seqfan] A242003

[israel at math.ubc.ca]

This is one of a number of similar recently-approved sequences from  	
Vaclav Kotesovec.  It is titled "G.f. satisfies: A(x) = x + A(x*A(x))", 
and with offset of 0 the data are given as 1, 1, 1, 3, ....  But the g.f. 
1 + x + x^2 + 3*x^3 + ... wouldn't satisfy the equation in the title.  
It seems to satisfy 2*A(x) = 1 + x + A(x*A(x)) instead.

For a power series A(x) to satisfy A(x) = x + A(x*A(x)), the coefficient
a(0) can be anything except 1.  The solution with a(0) = 0 would be
x+x^2+x^3+2*x^4+4*x^5+8*x^6+17*x^7+38*x^8+87*x^9+203*x^10+482*x^11+...
The sequence of coefficients here is A006196 (and the fact that the g.f.
of this sequence satisfies A(x) = x + A(x*A(x)) is noted there).

So, what to do with A242003?

I haven't checked the other sequences in this group.  Someone should.

Cheers,
Robert