# [seqfan] Re: Generating function for A000992

Paul D Hanna pauldhanna at juno.com
Tue Dec 20 22:01:52 CET 2011

```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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