#ALL THE WAYS OF MAKING CHANGE 

#Doron Zeilberger, Rutgers University., 
#DoronZeil at gmail dot com

Make_Change:=proc(AMOUNT,NUMBER_OF_COINS):

convert(
 expand(
  coeff(
  taylor(
    coeff(
    taylor(
          1/(1-t*Penny*q)/(1-t*Nickel*q^5)/(1-t*Dime*q^10)/
          (1-t*Quarter*q^25)/(1-t*Half_Dollar*q^50)/(1-t*Dollar*q^100),
          t=0,NUMBER_OF_COINS+1
          ), t,NUMBER_OF_COINS
         ), q=0,AMOUNT+1
        ),q,AMOUNT
       )
      ),set
     ):
end: