[seqfan] Formula for A228608

[Paul D Hanna]

SeqFans, 
       Can someone see a more simple formula for http://oeis.org/A228608  
where e.g.f. A(x) satisfies: 
      A'(x) = A(x)^2 + A(x)^4.  
         
I found 
    log(A(x)) = Series_Reversion( 1-exp(-x) - atan(tanh(x/2)) ) 
but it seems there should be a simpler expression. 
          
A variant is http://oeis.org/A124214    where e.g.f. A(x) satisfies 
    A'(x) = A(x) + A(x)^4, 
and for this there exists the explicit formula 
    A(x) = exp(x) / (2 - exp(3*x))^(1/3). 
        
Perhaps a similar explicit formula also exists for A228608?  
     Paul