## combinatorics convolution, is this correct?

how many ways to make change for n dollars using pennies and nickels?

i.e.

what is the coefficient of the x^100n term in

(1+x+x^2+...+x^100n) * (1+x^5+x^10+...+x^100n)?

for the sake of clarity, I rewrote the sums as finite geometric series using sigma notation. by inspection one can see (i think) that the coefficient of x^100n in the above product would be

1 + 20n ways

have i done this correctly?