[seqfan] Re: Observation on A080936

[Neil Sloane]

David, I think it is better to create a new sequence
which has that extra first column. With cross-references
between them.
There are several reasons (e.g. the way the OEIS handles triangles,
addi ng a column makes a huge
difference to the linearized version).
Thanks
Neil

On Tue, Sep 4, 2012 at 6:26 PM, David Wilson <davidwwilson at comcast.net>wrote:

>
> For A080936, T(n,k) also counts the number of balanced stings of n pairs
> parentheses having nesting depth k.
>
> For example, for 3 pairs of parentheses, there are 5 balanced strings
>
> ()()(), ()(()), (()()), (())(), ((()))
>
> with nesting depths 1, 2, 2, 2, 3 respectively, so that
>
> T(3,1) = 1
> T(3,2) = 3
> T(3,3) = 1
>
> I think that there is probably a simple bijection to Dyck paths that makes
> this clear.
>
> The current table is
>
> 1;
> 1,1;
> 1,3,1;
> 1,7,5,1;
> 1,15,18,7,1;
> 1,31,57,33,9,1;
> 1,63,169,132,52,11,1;
>
> I think a zero row and column should be added to give
>
> 1;
> 0,1;
> 0,1,1;
> 0,1,3,1;
>
> &c.
>
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-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com