A155993 A triangle of polynomial coefficients: p(x,n)=-(ChebyshevT[n, x] - ((x + 1)^n + (1 - x)^n)); sp(x,n) = p(x, n) + x^n*p(1/x, n).

2, 1, 1, 3, 0, 3, -2, 9, 9, -2, -5, 0, 40, 0, -5, -14, 5, 40, 40, 5, -14, -27, 0, 90, 0, 90, 0, -27, -62, 21, 154, 14, 14, 154, 21, -62, -125, 0, 400, 0, -40, 0, 400, 0, -125, -254, 9, 648, 288, -180, -180, 288, 648, 9, -254, -507, 0, 1410, 0, 120, 0, 120, 0, 1410, 0, -507

Offset

0,1

Comments

Row sums are:

{2, 2, 6, 14, 30, 62, 126, 254, 510, 1022, 2046,...}.

Links

Table of n, a(n) for n=0..65.

Formula

p(x,n)=-(ChebyshevT[n, x] - ((x + 1)^n + (1 - x)^n));

sp(x,n) = p(x, n) + x^n*p(1/x, n).

Example

{2},
{1, 1},
{3, 0, 3},
{-2, 9, 9, -2},
{-5, 0, 40, 0, -5},
{-14, 5, 40, 40, 5, -14},
{-27, 0, 90, 0, 90, 0, -27},
{-62, 21, 154, 14, 14, 154, 21, -62},
{-125, 0, 400, 0, -40, 0, 400, 0, -125},
{-254, 9, 648, 288, -180, -180, 288, 648, 9, -254},
{-507, 0, 1410, 0, 120, 0, 120, 0, 1410, 0, -507}

Mathematica

p[x_, n_] = -(ChebyshevT[n, x] - ((x + 1)^n + (1 - x)^n));
sp[x_, n_] = p[x, n] + x^n*p[1/x, n];
Table[FullSimplify[ExpandAll[sp[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[sp[x, n]]], x], {n, 0, 10}]; Q Flatten[%]

Crossrefs

Sequence in context: A033774 A033804 A103910 * A353630 A341091 A210806

Adjacent sequences: A155990 A155991 A155992 * A155994 A155995 A155996

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Feb 01 2009

Status

approved