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 A128411 Coefficient array for orthogonal polynomials defined by C(2n,n). 2

%I #2 Mar 30 2012 18:59:20

%S 1,-2,1,4,-8,2,-8,36,-24,4,16,-128,160,-64,8,-32,400,-800,560,-160,16,

%T 64,-1152,3360,-3584,1728,-384,32,-128,3136,-12544,18816,-13440,4928,

%U -896,64,256,-8192,43008,-86016,84480,-45056,13312

%N Coefficient array for orthogonal polynomials defined by C(2n,n).

%C Define {p(n,x)} to be the family of orthogonal polynomials on [0,4] for the weight function (1/pi)*1/sqrt(x(4-x)) which defines C(2n,n). We have p(n,x)=(2x-4)*p(n-1,x)-4*p(n-2,x), with p(0,x)=1, p(1,x)=-2+x. A scaled version of this triangle is given by A128412.

%F Column k has g.f. if(k=0,1/(1+2x),(1-2x)*((2^(k-1)+0^k/2)*x^k/(1+2x)^(2k+1))).

%F T(n,k)=(C(n+k,n-k)(-1)^(n-k)-C(n+k-1,n-k-1)(-1)^(n-k-1))*(2^(n-1)+0^n/2); T(n,k)=A110162(n,k)*(2^(n-1)+0^n/2); - _Paul Barry_, Mar 22 2007

%e Triangle begins

%e 1,

%e -2, 1,

%e 4, -8, 2,

%e -8, 36, -24, 4,

%e 16, -128, 160, -64, 8,

%e -32, 400, -800, 560, -160, 16,

%e 64, -1152, 3360, -3584, 1728, -384, 32

%K easy,sign,tabl

%O 0,2

%A _Paul Barry_, Mar 02 2007

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Last modified October 3 10:22 EDT 2023. Contains 365859 sequences. (Running on oeis4.)