[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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