This question is similar to another that I asked, but should be, I think, very much easier.

Start with the generating function for unrestricted partitions and replace some of the plus signs with minus signs to get: ( +/- means plus or minus )

(1 +/- x +/- x^2 +/- x^3 +/- ...)(1 +/- x^2 +/- x^4 +/- x^6 +/- ...) (1 +/- x^3 +/- x^6 +/- x^9 +/- ...) ... Multiply everything out to give:

1 + a(1) x + a(2) x^2 + a(3) x^3 +...

For a given positive integer, n, is it always possible to choose the signs such that a(n) is equal to +1 or 0 or -1?

My previous question on the same topic asked if it is possible to choose the signs such that every coefficient in the series is +1, 0, or -1.

I'm convinced that the answer to this question is yes.