A178103 Coefficient array of orthogonal polynomials P(n,x)=x*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1,P(1,x)=x.

1, 0, 1, -1, 0, 1, 0, -4, 0, 1, 5, 0, -9, 0, 1, 0, 33, 0, -16, 0, 1, -45, 0, 114, 0, -25, 0, 1, 0, -408, 0, 290, 0, -36, 0, 1, 585, 0, -1890, 0, 615, 0, -49, 0, 1, 0, 6705, 0, -6240, 0, 1155, 0, -64, 0, 1, -9945, 0, 38835, 0, -16695, 0, 1988, 0, -81, 0, 1, 0, -137340, 0, 157395, 0

Offset: 0

Author

Paul Barry, May 20 2010

Keywords

• sign
• tabl

Comments

First row is aerated signed version of quartic factorial numbers A007696. Inverse is A178104.

Examples

			Triangle begins
1,
0, 1,
-1, 0, 1,
0, -4, 0, 1,
5, 0, -9, 0, 1,
0, 33, 0, -16, 0, 1,
-45, 0, 114, 0, -25, 0, 1,
0, -408, 0, 290, 0, -36, 0, 1,
585, 0, -1890, 0, 615, 0, -49, 0, 1
Production matrix of inverse is
0, 1,
1, 0, 1,
0, 3, 0, 1,
0, 0, 5, 0, 1,
0, 0, 0, 7, 0, 1,
0, 0, 0, 0, 9, 0, 1,
0, 0, 0, 0, 0, 11, 0, 1,
0, 0, 0, 0, 0, 0, 13, 0, 1,
0, 0, 0, 0, 0, 0, 0, 15, 0, 1