A137430 Triangular sequence from coefficients of a cumulative sum of Chebyshev T(x,n) polynomials (A053120): p(x,n)=p(x,n-1)+T(x,n).

1, 1, 1, 0, 1, 2, 0, -2, 2, 4, 1, -2, -6, 4, 8, 1, 3, -6, -16, 8, 16, 0, 3, 12, -16, -40, 16, 32, 0, -4, 12, 40, -40, -96, 32, 64, 1, -4, -20, 40, 120, -96, -224, 64, 128, 1, 5, -20, -80, 120, 336, -224, -512, 128, 256, 0, 5, 30, -80, -280, 336, 896, -512, -1152, 256, 512

Offset: 1

Author

Roger L. Bagula, Apr 27 2008

Keywords

• tabl
• sign

Comments

Row sums are: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

Examples

			{1},
{1, 1},
{0, 1, 2},
{0, -2, 2, 4},
{1, -2, -6, 4, 8},
{1, 3, -6, -16, 8, 6},
{0, 3, 12, -16, -40, 16, 32},
{0, -4, 12, 40, -40, -96, 32, 64},
{1, -4, -20, 40, 120, -96, -224, 64, 128},
{1, 5, -20, -80, 120, 336, -224, -512, 128, 256},
{0, 5, 30, -80, -280, 336,896, -512, -1152, 256, 512}
		

Crossrefs

Cf. A053120.

Programs

Mathematica

Clear[P] P[x, -1] = 0; P[x, 0] = 1; P[x_, n_] := P[x, n] = P[x, n - 1] + ChebyshevT[n, x]; Table[P[x, n], {n, 0, 10}]; a = Table[CoefficientList[P[x, n], x], {n, 0, 10}]; Flatten[a]

Formula

p(x,n)=p(x,n-1)+T(x,n); out_n,m=Coefficients(p(x,n)).