A178090 Coefficient array for orthogonal polynomials P(n,x)=x*P(n-1,x)-floor((n-1)/2)*P(n-2,x), P(0,x)=1,P(1,x)=x.

1, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, -2, 0, 1, 0, 2, 0, -4, 0, 1, 0, 0, 6, 0, -6, 0, 1, 0, -6, 0, 18, 0, -9, 0, 1, 0, 0, -24, 0, 36, 0, -12, 0, 1, 0, 24, 0, -96, 0, 72, 0, -16, 0, 1, 0, 0, 120, 0, -240, 0, 120, 0, -20, 0, 1, 0, -120, 0, 600, 0, -600, 0, 200, 0, -25, 0, 1, 0, 0, -720, 0

Offset

0,13

Comments

Inverse is the unsigned version.

Links

Table of n, a(n) for n=0..81.

Formula

T(n,k)=[k<=n]*((1+(-1)^(n-k))/2)*((n-k)/2)!*C((n+k)/2-1-floor((k-1)/2), (n+k)/2-1-floor((k-1)/2)-floor(k/2))

*C((n+k)/2-1-floor(k/2),(n+k)/2-1-floor(k/2)-floor((k-1)/2))*(-1)^((n-k)/2).

Example

Triangle begins
1,
0, 1,
0, 0, 1,
0, -1, 0, 1,
0, 0, -2, 0, 1,
0, 2, 0, -4, 0, 1,
0, 0, 6, 0, -6, 0, 1,
0, -6, 0, 18, 0, -9, 0, 1,
0, 0, -24, 0, 36, 0, -12, 0, 1,
0, 24, 0, -96, 0, 72, 0, -16, 0, 1,
0, 0, 120, 0, -240, 0, 120, 0, -20, 0, 1,
0, -120, 0, 600, 0, -600, 0, 200, 0, -25, 0, 1,
0, 0, -720, 0, 1800, 0, -1200, 0, 300, 0, -30, 0, 1
Product matrix of inverse is
0, 1,
0, 0, 1,
0, 1, 0, 1,
0, 0, 1, 0, 1,
0, 0, 0, 2, 0, 1,
0, 0, 0, 0, 2, 0, 1,
0, 0, 0, 0, 0, 3, 0, 1,
0, 0, 0, 0, 0, 0, 3, 0, 1,
0, 0, 0, 0, 0, 0, 0, 4, 0, 1

Crossrefs

Sequence in context: A054014 A158945 A156667 * A110914 A219200 A341978

Adjacent sequences: A178087 A178088 A178089 * A178091 A178092 A178093

Keyword

easy,sign,tabl

Author

Paul Barry, May 19 2010

Status

approved