How to change the summation form?

I have  sum((r+1)*(r+2)*(r+3)*(r+4)*F(r+4)*(k-r+1)*F(k-r+1), r = 0 .. k) =c (constant); 

outputs: for k=0,1,2,...

                        24 F(4) F(1) = c
                48 F(4) F(2) + 120 F(5) F(1) = c
        72 F(4) F(3) + 240 F(5) F(2) + 360 F(6) F(1) = c....

but I  need the alternate form

F(4)=c/24*F(1),

F(5)=(c-48F(4)F(2))/120*F(1),

F(6)=(c-72*F(4)*F(3)-240*F(5)*F(2))/360*F(1).....

How to change this?