The coefficients in the polynomial [an choose k]_q mod (qⁿ-1), may be found explicitly. There is another interpretation of these coefficients. For example, the constant term is the number of double cosets C_n \ S_an / (S_k x S_an-k). A multiset and Schur function version is also given. A positive polynomial q-version is conjectured which agrees with a known result on double cosets for GL_n(q) and the Singer cycle.