[seqfan] Re: Displaying an o.g.f for binomial(mn,n)

[Max Alekseyev]

Hi Tom,

This is not about your question but just a side note:

The expression looks to me unnecessarily cryptic. I believe a simpler
one can be obtained from series multisection
http://en.wikipedia.org/wiki/Series_multisection#Example of
(1+x)^{4n}.
Also the internal product seems to be simply the square root of
discriminant of the polynomial x^4-x+z w.r.t. x (which can be computed
even without knowing zeroes of the polynomial) - why not rewrite it
this way?

Regards,
Max

On Fri, May 25, 2012 at 3:34 PM, Thomas Copeland <tccopeland at gmail.com> wrote:
> Dear OEIS editors,
>
> Could someone please show me how to format the LaTeX expression below
> acceptably for the OEIS?
>
> It represents an apparent o.g.f. (z>=0) for the sequence
> binomial(4n,n), A005810. (It's integral is related to the associated
> Fuss-Catalan/Raney sequence A002293.)  I'd like to submit similar
> expressions for binomial(mn,n) for m=2,3, ....
>
> Please paste the following expression in the LaTeX editor at
> http://www.codecogs.com/latex/eqneditor.php to display it:
>
>
> o.g.f.(z^3)=\frac{1}{2\sqrt\Delta}\sum_{i= 1}^{4}\prod_{j,k\neq
> i,j<k}^{4}|x_j-x_k|
>
>
> where the x_k are the four zeros for   x^4-x+z=0 and delta is the
> discriminant |256-27z^3|^(1/2).
>
> Sincerely,
> Tom Copeland
>
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