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Search: id:A136663
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| A136663 |
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Triangle of coefficients of the Pascal sum of A053120 Chebyshev's T(n, x) polynomials :p(x,n)=2*x*p(x,n-1)-p(x,n-2); pp(x,n)=Sum[Binomial[n,m]*p(x,m),{m,0,n}]. |
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+0
1
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| 1, 1, 1, 0, 2, 2, -2, 0, 6, 4, -4, -8, 4, 16, 8, -4, -20, -20, 20, 40, 16, 0, -24, -72, -40, 72, 96, 32, 8, 0, -112, -224, -56, 224, 224, 64, 16, 64, -32, -448, -624, 0, 640, 512, 128, 16, 144, 288, -288, -1584, -1584, 384, 1728, 1152, 256, 0, 160, 800, 960, -1600, -5088, -3680, 1920, 4480, 2560, 512
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums:
{1, 0, -2, -6, -14, -30, -62, -126, -254, -510, -1022}
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FORMULA
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p(x,n)=2*x*p(x,n-1)-p(x,n-2); pp(x,n)=Sum[Binomial[n,m]*p(x,m),{m,0,n}]
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EXAMPLE
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{1},
{1, 1},
{0, 2, 2},
{-2, 0, 6, 4},
{-4, -8, 4, 16, 8},
{-4, -20, -20, 20, 40, 16},
{0, -24, -72, -40, 72, 96, 32},
{8, 0, -112, -224, -56, 224, 224, 64},
{16, 64, -32, -448, -624, 0, 640, 512, 128},
{16, 144, 288, -288, -1584, -1584, 384, 1728, 1152, 256},
{0,160, 800, 960, -1600, -5088, -3680, 1920, 4480, 2560, 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] - P[x, n - 2]; Q[x_, n_] := Q[x, n] = Sum[P[x, m]*Binomial[n, m], {m, 0, n}]; a = Table[CoefficientList[Q[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Cf. A053120.
Sequence in context: A082835 A104241 A011139 this_sequence A131079 A078336 A076441
Adjacent sequences: A136660 A136661 A136662 this_sequence A136664 A136665 A136666
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 02 2008
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