[seqfan] Re: Surprising Patterns in Tangent and Secant Numbers

[Paul D Hanna]

SeqFans, 
     I suppose that the proofs of the main observations in my prior email 
could start with establishing the following identity (in PARI notation): 
   
x/serreverse(x*serlaplace(exp(x)/cosh(x))) 
 
= x + x/serreverse(x*serlaplace(1/cosh(x)))
 
= 1 + x - x^2 + 3*x^4 - 38*x^6 + 947*x^8 - 37394*x^10 +...
  
Is this identity easy to prove? 
      Paul 
 
Cf. A157308.