What is the value of [n]n for n! and how can n! be written as a polynomial in n using the Stirling numbers of the first kind? Explicitly for n=6.
a) [6]6 = 720; n! = S(6,1)*6! + S(6,2)*5! + S(6,3)*4! + S(6,4)*3! + S(6,5)*2! + S(6,6)*1!
b) [6]6 = 720; n! = S(6,1)*1! + S(6,2)*2! + S(6,3)*3! + S(6,4)*4! + S(6,5)*5! + S(6,6)*6!
c) [6]6 = 720; n! = S(6,1)*6 + S(6,2)*15 + S(6,3)*20 + S(6,4)*15 + S(6,5)*6 + S(6,6)*1
d) [6]6 = 720; n! = S(6,1)*6^6 + S(6,2)*5^5 + S(6,3)*4^4 + S(6,4)*3^3 + S(6,5)*2^2 + S(6,6)*1^1
