[seqfan] Re: Polynomials in Seres Reversion of a Famiy of Function s

Paul D Hanna pauldhanna at juno.com
Wed Jul 25 07:35:59 CEST 2012


Sorry; Correction:  P(y,n) = Series_Reversion( G(y,n) - 1 )  has been made below. 
[NOT:    P(y,n) = Series_Reversion( G(y,n) )   as I wrote it in my prior email.] 
 
---------- Original Message ----------
From: "Paul D Hanna" <pauldhanna at juno.com>
To: seqfan at list.seqfan.eu
Subject: Re: [seqfan] Re: Polynomials in Seres Reversion of a Famiy of Function s
Date: Wed, 25 Jul 2012 05:26:54 GMT

Hello Gerard, 
     Your hints were sufficient to arrive at the g.f. of the new triangle A214670: 
 
   A(x,y) = Sum_{n>=1} -x^n * Product_{k=1..n} (1 - (1+y)^k) / (1 - x*(1+y)^k)  
  
in which row n is the finite polynomial P(y,n) defined by:  
   A(x,y) = Sum_{n>=1} x^n * P(y,n) 
such that: 
   P(y,n) = Series_Reversion( G(y,n) - 1 )  
where G(y,n) satisfies: 
   y = Sum_{m>=1} 1/G(y,n)^(n*m) * Product_{k=1..n} (1 - 1/G(y,n)^k), 
for n>=1. 
 
Thank you for your insights! 
     Paul 
[...] 



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