A078996 Triangle read by rows: let f(x) = x/(1-x-x^2); n-th row gives coefficients of denominator polynomial of n-th derivative f(x)^(n), with highest powers first, for n >= 0.

-1, -1, 1, 1, 2, -1, -2, 1, 1, 3, 0, -5, 0, 3, -1, 1, 4, 2, -8, -5, 8, 2, -4, 1, 1, 5, 5, -10, -15, 11, 15, -10, -5, 5, -1, 1, 6, 9, -10, -30, 6, 41, -6, -30, 10, 9, -6, 1, 1, 7, 14, -7, -49, -14, 77, 29, -77, -14, 49, -7, -14, 7, -1, 1, 8, 20, 0, -70, -56, 112, 120, -125, -120, 112, 56, -70, 0, 20, -8, 1

Offset: 0

Author

Mohammad K. Azarian, Jan 12 2003

Keywords

• sign
• tabf

Examples

			Triangle begins:
  -1, -1,  1;
   1,  2, -1, -2,  1;
   1,  3,  0, -5,  0,  3, -1;
  ...
		

Crossrefs

See A084610 for another version of this triangle.

Formula

f(x)^(n), for n=0, 1, 2, 3, 4, ..., where f(x)= x/(1-x-x^2).

G.f.: G(0)/(2*x) - 1/x - 2 - 2*x + 2*x^2 , where G(k)= 1 + 1/( 1 - (1+x-x^2)*x^(2*k+1)/((1+x-x^2)*x^(2*k+1) + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 06 2013

Extensions

Edited by N. J. A. Sloane, Jan 15 2011