After: http://list.seqfan.eu/pipermail/seqfan/2017-December/018190.html For case n=9=3^2, it appears the missing sequence is generated by a function F_3(x), written as: F_1(x) = 1/(1-x)^9 F_2(x) = x^3 * (2 - x^3)/(x^3 - 1)^2 F_3(x) = F_1/(1+F_2) = (1 + x + x^2)^2/(1 - x)^7 ( notice that F_2(x) can be written as a function of x^3 ) --Brad