[seqfan] Re: In the vein of 103314

[Chai Wah Wu]

Another possible formula:

For k >= 0, the 2^(k+1)-th row are the figurate numbers based on the
2^k-dimensional regular convex polytope with G.F.:
(1+x)^(2^k-1)/(1-x)^(2^k+1).

(See A000027, A000290, A014820, A099195)

Chai Wah

On Fri, Dec 22, 2017 at 2:24 AM, Frank Adams-Watters via SeqFan <
seqfan at list.seqfan.eu> wrote:

> I believe that in this case Max's earlier argument can be carried through
> to show that Chai's comment is correct.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Chai Wah Wu <cwwuieee at gmail.com>
> To: seqfan <seqfan at list.seqfan.eu>
> Sent: Fri, Dec 22, 2017 12:11 am
> Subject: [seqfan] Re: In the vein of 103314
>
> It appears that for p prime, the p-th row corresponds to
> binomial(k+p-1,p-1) for k = 0,1,2,3,....
> which is the maximum possible (i.e. the number of combinations with
> repetitions of k choices from p categories).
>
> Chai Wah
>
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