I am struggling with finding a recursive definition of the following:
$$a_0 = 1$$ $$a_1 = -(nx-1)$$ $$a_2 = (n+1)*x*(nx-2)+1$$ $$a_3 = -((n+2)*x*((n+1)*x*(nx-3)+3)-1)$$ $$a_4 = ((n+3)*x*((n+2)*x*((n+1)*x*(nx-4)+6)-4)+1)$$ ...
There is a certain pattern for sure, however I'm not able to convert it into a recursive definition.