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A136665 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). 0
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; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums:

{1, 1, 0, -3, -6, 3, 42, 63, -210, -987, 126}

LINKS

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

FORMULA

p(x,n)=2*x*p(x,n-1)-n*p(x,n-2).

EXAMPLE

{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}

MATHEMATICA

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]

CROSSREFS

Cf. A053120.

Sequence in context: A175950 A066285 A327873 * A047765 A068463 A099554

Adjacent sequences:  A136662 A136663 A136664 * A136666 A136667 A136668

KEYWORD

uned,tabl,sign

AUTHOR

Roger L. Bagula, Apr 02 2008

STATUS

approved

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Last modified April 3 16:46 EDT 2020. Contains 333197 sequences. (Running on oeis4.)