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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 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

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