asking for help

[Emeric Deutsch]

It seems that just asking the question has a good
effect on my brain.
Expand the "extra" 1/(1-4z) to get

SUM(4^j * binom(2n+q-2j,n-j),j=0..n).

Any "more" closed form?

Emeric



On Thu, 22 Mar 2007, Emeric Deutsch wrote:

> Dear seqfans,
> The following is well-known:
>
> If C(z)=[1-sqrt(1-4z)]/(2z) is the Catalan function, then
> the coefficient of z^n in the expansion of C^q/sqrt(1-4z)
> is binom(2n+q,n).
>
> Is anything known about
>
> the coefficient of z^n in the expansion of C^q/(1-4z)^(3/2) ?
>
> For the cases q=1, q=2, q=3 there are formulas in
> A000531, A029760, A045720, respectively.
>
> Many thanks for any information you may have.
>
> Emeric
>
>
>
>