[seqfan] Re: Generalized Pascal triangle needs a recurrence

[Max Alekseyev]

I do not see how it generalizes Pascal's triangle -- could you please
explain this relationship?
Thanks,
Max

On Tue, May 7, 2013 at 2:43 PM, Neil Sloane <njasloane at gmail.com> wrote:
> Dear SeqFans,
> Roger Bagula has constructed some interesting triangles that
> generalize Pascal's triangle (A007318), but his constructions are
> fairly complicated. It would be nice to have a direct construction
> like that for Pascal's triangle.
> The first of them is in A159041.
>
> This triangle begins:
> {1},
> {1, 1},
> {1, -10, 1},
> {1, -25, -25, 1},
> {1, -56, 246, -56, 1},
> {1, -119, 1072, 1072, -119, 1},
> {1, -246, 4047, -11572, 4047, -246, 1},
> {1, -501, 14107, -74127, -74127, 14107, -501, 1},
> {1, -1012, 46828, -408364, 901990, -408364, 46828, -1012, 1},
> {1, -2035, 150602, -2052886, 7685228, 7685228, -2052886, 150602, -2035, 1},
> { 1, -4082, 474189, -9713496, 56604978, -105907308, 56604978,
> -9713496, 474189, -4082, 1}
>
> Can anyone see a recurrence? I can't.
> (The second column is easy)
> There's a Mma program that will produce more terms if they are needed.
> Neil
>
> --
> 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
>
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