  We consider vector spaces H(n,l) and F(n,l) spanned by the degree-n
coefficients in power series forms of the Homfly and Kauffman polynomials of
links with l components. Generalizing previously known formulas, we determine
the dimensions of the spaces H(n,l), F(n,l) and H(n,l)+F(n,l) for all values of
n and l. Furthermore, we show that for knots the algebra generated by
H(n,1)+F(n,1) (n > 0) is a polynomial algebra with
dim(H(n,1)+F(n,1))-1=n+[n/2]-4 generators in degree n>3 and one generator in
degrees 2 and 3.
