  Starting with a definition based on the Catalan numbers, we carry out an
empirical study of the Rueppel sequence. We use the Hankel transform as the
main technique. By means of this transform we find links to such sequences as
the Jacobi sequence and the paper-folding sequence. We also study several
number arrays defined by this sequence, which are analogs of the important
Catalan triangles of combinatorics. We identify a sequence related to the
Golay-Rudin-Shapiro sequence that plays a fundamental role in linking the
Hankel transforms of the paper with classical sequences. Examples are given
where certain privileged permutations appearing in the Leibnitz formula for
determinants have a special role.
