Specializations of Schur functions at consecutive integers
Given a partition λ = (λ1, λ2, ..., λn) denote with sλ the associated Schur function. There exists a nice product formula for the principal specializations:
sλ(1, q, q2, ..., qn-1) = Πi<j (qλi+n-i - qλj+n-j) / (qj-1 - qi-1).
Is a similar evaluation known for specializations of the type sλ(1, 2, ..., n)?