OFFSET
0,1
COMMENTS
Row sums are:
{-2, 0, 2, 8, 22, 52, 114, 240, 494, 1004, 2026,...}.
FORMULA
p(x,n)=-(ChebyshevU[n, x] - ((x + 1)^n - (1 - x)^n));
sp(x,n) = p(x, n) + x^n*p(1/x, n).
EXAMPLE
{-2},
{},
{-3, 8, -3},
{-6, 10, 10, -6},
{-17, 16, 24, 16, -17},
{-30, 4, 52, 52, 4, -30},
{-63, 24, 56, 80, 56, 24, -63},
{-126, 22, 234, -10, -10, 234, 22, -126},
{-257, 32, 488, 224, -480, 224, 488, 32, -257},
{-510, 8, 1096, 328, -420, -420, 328, 1096, 8, -510},
{-1023, 40, 2244, 480, -1232, 1008, -1232, 480, 2244, 40, -1023}
MATHEMATICA
p[x_, n_] =-(ChebyshevU[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
KEYWORD
AUTHOR
Roger L. Bagula, Feb 01 2009
STATUS
approved