The expansion of the 4th power binomially uses the coefficients 1 4 6 4 1, so A=C=4 and B=6.
n=4
Coefficients are n, n(n-1)/2!, n(n-1)(n-2)/3!=n in the binomial expansion. 1 4 6 4 1 is the 4th row of Pascal's Triangle:
........1
...1...2...1
..1 3....3 1
.1 4..6..4 1
1 5 10 10 5 1
.......etc........