  Let $K$ denote a field, and let $V$ denote a vector space over $K$ with
finite positive dimension. We consider a pair of linear transformations $A:V
\to V$ and $A^*:V \to V$ that satisfy (i), (ii) below:
  (i) There exists a basis for $V$ with respect to which the matrix
representing $A$ is irreducible tridiagonal and the matrix representing $A^*$
is diagonal.
  (ii) There exists a basis for $V$ with respect to which the matrix
representing $A^*$ is irreducible tridiagonal and the matrix representing $A$
is diagonal.
  We call such a pair a {\em Leonard pair} on $V$. In the literature on Leonard
pairs there exist two parameter sequences called the first split sequence and
the second split sequence. We display some attractive formulae for the first
and second split sequence that involve the trace function.
