Your last statement is correct. For example see the last page of www.math.hawaii.edu/~pavel/gen_functions.pdf . Victor On Fri, Jun 1, 2012 at 9:27 AM, Kimberling, Clark <ck6@evansville.edu>wrote:
Hello -
Suppose that a(0), a(1), a(2), ... is a linear recurrence sequence with generating function p(x)/q(x), and that b(0), b(1), b(2), ... is a linear recurrence sequence with generating function u(x)/v(x).
Does someone know a generating function for the product sequence a(0)*b(0), a(1)*b(1), a(2)*b*2), ... ?
It appears that a denominator may be a polynomial whose roots are the reciprocal-products 1/(r(i)*s(j)), where r(I) ranges through all the roots of q(x) and s(j) ranges through all the roots of v(x).
Clark Kimberling
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