OFFSET
1,5
COMMENTS
The degree of the polynomial in row n > 1 is 2^(n-1) - 1, hence the number of coefficients in row n >= 1 is given by 2^(n-1) = A000079(n-1).
For n > 1 a new row begins always with -1 and ends always with 1.
The coefficients in row n are the first k negative coefficients in row n+1 in A225200.
The sum and product of the generalized sequence of fractions given by m^(2^(n-2)) divided by the polynomial p(n) are equal, i.e.,
m + m/(m-1) = m * m/(m-1) = m^2/(m-1);
m + m/(m-1) + m^2/(m^2-m+1) = m * (m/(m-1)) * m^2/(m^2-m+1) = m^4/(m^3-2*m^2+2*m-1).
EXAMPLE
The triangle T(n,k), k = 0..2^(n-1)-1, begins
1;
-1, 1;
-1, 2, -2, 1;
-1, 4, -8, 10, -9, 6, -3, 1;
-1, 8, -32, 84, -162, 244, -298, 302, -258, 188, -118, 64, -30, 12, -4, 1;
MAPLE
b:=proc(n) option remember; b(n-1)-b(n-1)^2; end;
b(1):=1/m;
a:=n->m^(2^(i-1))*normal(b(i));
seq(op(PolynomialTools[CoefficientList](a(i), m, termorder=forward)), i=1..6);
CROSSREFS
KEYWORD
sign,tabf
AUTHOR
Martin Renner, May 01 2013
STATUS
approved