[seqfan] Seq A144005 = A014623 ?

[Paul D Hanna]

SeqFans, 
      This most likely is a coincidence of initial terms, but are these sequences essentially the same?  
http://oeis.org/A014623 -   
Sequence arising from analysis of Levine's sequence A011784.
 
http://oeis.org/A144005 -  
E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral A(-x) dx ).
 
Both of these begin (making allowances for offset): 
1, 1, 2, 7, 33, 201, 1479, 12842, 127952, ... 
 
Does anyone know how Colin Mallows arrived at these terms from Levine's sequence? 
 
I'm copying Colin Mallows (given the email address is still correct), the author of A014623. 
  
Thanks,  
    Paul