OFFSET
0,13
COMMENTS
Coefficient array of orthogonal polynomials P(n,x)=xP(n-1,x)-((1+(-1)^n)/2)*P(n-2,x), P(0,x)=1,P(1,x)=x.
Inverse is A178112.
EXAMPLE
Triangle begins
1,
0, 1,
-1, 0, 1,
0, -1, 0, 1,
1, 0, -2, 0, 1,
0, 1, 0, -2, 0, 1,
-1, 0, 3, 0, -3, 0, 1,
0, -1, 0, 3, 0, -3, 0, 1,
1, 0, -4, 0, 6, 0, -4, 0, 1,
0, 1, 0, -4, 0, 6, 0, -4, 0, 1,
-1, 0, 5, 0, -10, 0, 10, 0, -5, 0, 1
Production matrix is
0, 1,
-1, 0, 1,
0, 0, 0, 1,
0, 0, -1, 0, 1,
0, 0, 0, 0, 0, 1,
0, 0, 0, 0, -1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, -1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1
Production matrix of inverse is
0, 1,
1, 0, 1,
0, 0, 0, 1,
0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 1,
0, 0, 0, 0, 0, 0, 1, 0, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1
MAPLE
P := (n, x) -> `if`(n < 2, x^n, x*P(n-1, x) - ((1+(-1)^n)/2)*P(n-2, x)):
ListTools:-Flatten([seq(PolynomialTools:-CoefficientList(P(n, x), x), n=0..12)]);
# Peter Luschny, Aug 10 2019
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, May 20 2010
STATUS
approved