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Search: id:A136665
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| A136665 |
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Triangle of coefficients of Hermite-like analog of A053120 Chebyshev's T(n, x) polynomials (powers of x in increasing order): p(x,n)=2*x*p(x,n-1)-n*p(x,n-2). |
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+0
1
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| 1, 0, 1, -2, 0, 2, 0, -7, 0, 4, 8, 0, -22, 0, 8, 0, 51, 0, -64, 0, 16, -48, 0, 234, 0, -176, 0, 32, 0, -453, 0, 916, 0, -464, 0, 64, 384, 0, -2778, 0, 3240, 0, -1184, 0, 128, 0, 4845, 0, -13800, 0, 10656, 0, -2944, 0, 256, -3840, 0, 37470, 0, -60000, 0, 33152, 0, -7168, 0, 512
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Row sums:
{1, 1, 0, -3, -6, 3, 42, 63, -210, -987, 126}
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FORMULA
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p(x,n)=2*x*p(x,n-1)-n*p(x,n-2).
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EXAMPLE
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{1},
{0, 1},
{-2, 0, 2},
{0, -7, 0, 4},
{8, 0, -22, 0, 8},
{0, 51, 0, -64, 0, 16},
{-48, 0, 234, 0, -176, 0, 32},
{0, -453, 0, 916, 0, -464,0, 64},
{384, 0, -2778, 0, 3240, 0, -1184, 0, 128},
{0, 4845, 0, -13800, 0, 10656, 0, -2944, 0,256},
{-3840, 0, 37470, 0, -60000, 0, 33152, 0, -7168, 0, 512}
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MATHEMATICA
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P[x, 0] = 1; P[x, 1] = x; P[x_, n_] := P[x, n] = 2*x*P[x, n - 1] - n*P[x, n - 2]; Table[ExpandAll[P[x, n]], {n, 0, 10}]; a = Table[CoefficientList[P[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Cf. A053120.
Sequence in context: A042970 A136581 A066285 this_sequence A047765 A068463 A099554
Adjacent sequences: A136662 A136663 A136664 this_sequence A136666 A136667 A136668
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 02 2008
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