For the mentioned family
of pretzel knots (2p+1),(2q+1),(2r+1)
D((2p+1),(2q+1),(2r+1))
= 

pqprqrr+(2pq+2pr+2qr+2r+1)t+(pqprqrr)t^{2}, 

and the Conway polynomial
is
C((2p+1),(2q+1),(2r+1))
= 1+(pqprqrr)x. 

For pq = pr+qr+r it follows
D =
1 and C = 1.
This points to the more
general conclusion: for every family of KLs we can derive a general formula
for Alexander polynomials, where the coefficients are expressed by numbers
appearing in a Conway symbol of the KLs. Later we will see that the same
holds for all polynomial invariants, but the formulas derived will be more
complicated.
Before returning to that
question and a series of similar questions about families and the regular
distribution of KL invariants (as signatures, symmetry groups, chirality,
unknotting and unlinking numbers,
etc.) we will continue with the
derivation of KLs in Conway notation. After that, we will be able to work
with all KLs, and not just with the already derived rational KLs.
