--the list of partial sums of ns
partialSums=\ns->zipWith (\x->\counter -> sum (take counter ns)) ns (from 1)

--the list of powers of n
powers= \n -> n:map(\x -> x*n) (powers n)

--the list of factorials
factorials= 1 : zipWith (\a ->\b -> a*b) (from 2) (factorials)