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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

%I

%S 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,

%T 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,

%U 0,-240,0,120,0,-20,0,1,0,-120,0,600,0,-600,0,200,0,-25,0,1,0,0,-720,0

%N 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.

%C Inverse is the unsigned version.

%F 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))

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

%e Triangle begins

%e 1,

%e 0, 1,

%e 0, 0, 1,

%e 0, -1, 0, 1,

%e 0, 0, -2, 0, 1,

%e 0, 2, 0, -4, 0, 1,

%e 0, 0, 6, 0, -6, 0, 1,

%e 0, -6, 0, 18, 0, -9, 0, 1,

%e 0, 0, -24, 0, 36, 0, -12, 0, 1,

%e 0, 24, 0, -96, 0, 72, 0, -16, 0, 1,

%e 0, 0, 120, 0, -240, 0, 120, 0, -20, 0, 1,

%e 0, -120, 0, 600, 0, -600, 0, 200, 0, -25, 0, 1,

%e 0, 0, -720, 0, 1800, 0, -1200, 0, 300, 0, -30, 0, 1

%e Product matrix of inverse is

%e 0, 1,

%e 0, 0, 1,

%e 0, 1, 0, 1,

%e 0, 0, 1, 0, 1,

%e 0, 0, 0, 2, 0, 1,

%e 0, 0, 0, 0, 2, 0, 1,

%e 0, 0, 0, 0, 0, 3, 0, 1,

%e 0, 0, 0, 0, 0, 0, 3, 0, 1,

%e 0, 0, 0, 0, 0, 0, 0, 4, 0, 1

%K easy,sign,tabl

%O 0,13

%A _Paul Barry_, May 19 2010

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Last modified May 23 10:05 EDT 2022. Contains 353975 sequences. (Running on oeis4.)