This baby was put together using the series' composition of multiples of three basic series:
U(a,b,c)F = aU(1,0,0)F + bU(0,1,0)F + cU(0,0,1)F
and Ed's formalization of 'Sigma repeated'.
With the substitution of property 6 it can be transformed into its 'factorial form'.
It gives the entire polynome and can be applied to calculate specific high-indexed terms without the need to develop the whole series involved.