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A136663 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}]. 1
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; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums:

{1, 0, -2, -6, -14, -30, -62, -126, -254, -510, -1022}

LINKS

Table of n, a(n) for n=1..66.

FORMULA

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}]

EXAMPLE

{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}

MATHEMATICA

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]

CROSSREFS

Cf. A053120.

Sequence in context: A082835 A104241 A011139 * A165490 A298819 A307520

Adjacent sequences:  A136660 A136661 A136662 * A136664 A136665 A136666

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Apr 02 2008

STATUS

approved

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Last modified October 16 13:10 EDT 2019. Contains 328069 sequences. (Running on oeis4.)