What is the number of solutions of $(a\_i)\_{i=1}^n$ such that
$$\sum\_{i=1}^nia\_i\le b,\quad a\_i\in\{-1,1\},\quad \sum\_{i=1}^n{a\_i}=c$$
given $b,c\in\mathbf Z$?


Is there a generating function solution?



Sign Enumeration
The g.f. equals
$$\frac1{1-y}\prod\_{i=1}^n \left(xy^i + (xy^i)^{-1}\right).$$
That is, the number of solutions is given by the coefficient of $x^cy^b$.


