Apply the forward INVERT transform to a fully captured signed integer sequence a...
https://datenvertrag.halowerk.com/v1/invert-sequence-prefixOverview
Apply the forward INVERT transform to a fully captured signed integer sequence a1,...,aN. The result b1,...,bN is defined by 1+B(x)=1/(1-A(x)), where A(x)=a1*x+...+aN*x^N and coefficients are retained through degree N. Equivalently, b_n is the sum, over all ordered compositions of n, of the product of the corresponding input entries. For example, [1,1,1,1] maps to [1,2,4,8], and [-1,0,0] maps to [-1,1,-1].