OFFSET
1,8
COMMENTS
The degree of the polynomial in row n > 1 is 2^(n-2), hence the number of coefficients in row n > 1 is given by 2^(n-2) + 1 = A094373(n-1).
For n > 2 a new row always begins and ends with 1.
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), begins
1;
-1, 1;
1, -1, 1;
1, -2, 2, -1, 1;
1, -4, 8, -10, 9, -6, 3, -1, 1;
MAPLE
b:=n->m^(2^(n-2)); # n > 1
b(1):=m;
p:=proc(n) option remember; p(n-1)*a(n-1); end;
p(1):=1;
a:=proc(n) option remember; b(n)-p(n); end;
a(1):=1;
seq(op(PolynomialTools[CoefficientList](a(i), m, termorder=forward)), i=1..7);
CROSSREFS
KEYWORD
sign,tabf
AUTHOR
Martin Renner, May 01 2013
STATUS
approved