

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).


0



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
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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 * A210806 A147867 A227431
Adjacent sequences: A155990 A155991 A155992 * A155994 A155995 A155996


KEYWORD

sign,tabl,uned


AUTHOR

Roger L. Bagula, Feb 01 2009


STATUS

approved



