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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.
0
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.
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
KEYWORD
easy,sign,tabl
AUTHOR
Paul Barry, May 19 2010
STATUS
approved