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Search: id:A128411
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| A128411 |
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Coefficient array for orthogonal polynomials defined by C(2n,n). |
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+0
3
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| 1, -2, 1, 4, -8, 2, -8, 36, -24, 4, 16, -128, 160, -64, 8, -32, 400, -800, 560, -160, 16, 64, -1152, 3360, -3584, 1728, -384, 32, -128, 3136, -12544, 18816, -13440, 4928, -896, 64, 256, -8192, 43008, -86016, 84480, -45056, 13312
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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FORMULA
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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))).
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 (pbarry(AT)wit.ie), Mar 22 2007
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EXAMPLE
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Triangle begins
1,
-2, 1,
4, -8, 2,
-8, 36, -24, 4,
16, -128, 160, -64, 8,
-32, 400, -800, 560, -160, 16,
64, -1152, 3360, -3584, 1728, -384, 32
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CROSSREFS
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Sequence in context: A128412 A071951 A160323 this_sequence A164614 A094511 A026204
Adjacent sequences: A128408 A128409 A128410 this_sequence A128412 A128413 A128414
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 02 2007
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