[seqfan] Re: Generating function for A000992

[Reinhard Zumkeller]

2011/12/20, Paul D Hanna <pauldhanna at juno.com>:
> There may be a more compact g.f. for A000992, but here is one approach.
>
> Let A(x) = Sum_{n>=0} A000992(n) * x^n, then
>
> 1 = (A(x) + A(-x))/2 * (1 - x*(A(x) - A(-x))/2)
>
> which is equivalent to:
>
> -2 + 2*A(x) - x*A(x)^2  =  2 - 2*A(-x) - x*A(-x)^2
>
> = Sum_{n>=0} A000992(n)^2 * x^(2*n+1)
>
> = x + x^3 + x^5 + 4*x^7 + 9*x^9 + 36*x^11 + 121*x^13 + 576*x^15 + 2209*x^17
> +...
>
> an odd function with coefficients equal to the squares of A000992(n).
>
> - Paul D. Hanna
>
> ---------- Original Message ----------
> From: "N. J. A. Sloane" <njas at research.att.com>
> To: seqfan at seqfan.eu
> Cc: njas at research.att.com
> Subject: [seqfan] Generating function for A000992
> Date: Tue, 20 Dec 2011 11:09:22 -0500
>
>
>
> Dear Sequence Fans,
> A correspondent asks if there is a formula or g.f. for A000992:
>
>> Date: Tue, 20 Dec 2011 12:50:41 +0100
>> From: Jan Schwientek <Jan.Schwientek at itwm.fraunhofer.de>
>> I'm PhD student and interested in an explicit representation and/or
>> generating function for the integer sequence A000992
>
> Can anyone help him?
> Neil
>
>
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