[seqfan] Generalized Pascal triangle needs a recurrence

[Neil Sloane]

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