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).

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

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: A339423 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