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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,13
COMMENTS
Inverse is the unsigned version.
LINKS
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

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Last modified March 3 07:49 EST 2024. Contains 370499 sequences. (Running on oeis4.)