A128412 A scaled version of the coefficient array for orthogonal polynomials defined by C(2n,n).

1, -2, 1, 4, -8, 1, -8, 36, -12, 1, 16, -128, 80, -16, 1, -32, 400, -400, 140, -20, 1, 64, -1152, 1680, -896, 216, -24, 1, -128, 3136, -6272, 4704, -1680, 308, -28, 1, 256, -8192, 21504, -21504, 10560, -2816

Offset: 0

Author

Paul Barry, Mar 02 2007

Keywords

• easy
• sign
• tabl

Comments

Inverse is A128413.

Examples

			Triangle begins:
  1,
  -2, 1,
  4, -8, 1,
  -8, 36, -12, 1,
  16, -128, 80, -16, 1,
  -32, 400, -400, 140, -20, 1,
  64, -1152, 1680, -896, 216, -24, 1,
  -128, 3136, -6272, 4704, -1680, 308, -28, 1,
  256, -8192, 21504, -21504, 10560, -2816, 416, -32, 1,
  -512, 20736, -69120, 88704, -57024, 20592, -4368, 540, -36, 1,
  1024, -51200, 211200, -337920, 274560, -128128, 36400, -6400, 680, -40, 1
		

Formula

Number triangle T(n,k)=A128411(n,k)/(2^(k-1)+0^k/2).

Column k has g.f. if(k=0,1/(1+2*x),(1-2*x)*x^k/(1+2*x)^(2*k+1)).