Franklin (and seqfans),
    Perhaps this is just coincidence, 
but so far the g.f. A(x) of the terms
> 1,1,1,2,4,7,13,24 
 
satisfies these 2 relations: 
 
(1) A(x) = 1/A(-x*A(x))
  
(2) x*A(x) = series_reversion(x*A(-x))
 
It would be curious (since unlikely) if these trends continue.

Paul
