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

0,8

Comments

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

Links

Table of n, a(n) for n=0..70.

Example

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

Crossrefs

Sequence in context: A143844 A186759 A065623 * A147309 A147308 A110064

Adjacent sequences: A178100 A178101 A178102 * A178104 A178105 A178106

Keyword

sign,tabl

Author

Paul Barry, May 20 2010

Status

approved