def METHOD_NAME(self, lam):
    r"""
    Return the orthogonal symmetric function ``o[lam]`` expanded in
    the Schur basis, where ``lam`` is a partition.
    TESTS:
    Check that this is the inverse::
        sage: o = SymmetricFunctions(QQ).o()
        sage: s = SymmetricFunctions(QQ).s()
        sage: all(o(s(o[la])) == o[la] for i in range(5) for la in Partitions(i))
        True
        sage: all(s(o(s[la])) == s[la] for i in range(5) for la in Partitions(i))
        True
    """
    R = self.base_ring()
    n = sum(lam)
    return self._s._from_dict({ mu: R.sum( (-1)**j * lrcalc.lrcoef_unsafe(lam, mu, nu)
                                           for nu in Partitions(2*j)
                                               if all(nu.arm_length(i,i) == nu.leg_length(i,i)+1
                                                      for i in range(nu.frobenius_rank()))
                                         )
                                for j in range(n//2+1) # // 2 for horizontal dominoes
                                for mu in Partitions(n-2*j) })