pls what is the factorial expansion for $\displaystyle (n+1)! $

thanks

as a follow-up;

$\displaystyle a_1=\frac{-2a_0}{2.1+2-1} $

$\displaystyle a_2=\frac{-3a_1}{3.2+3-1} $

can the denominatior be equivalent to $\displaystyle (n+1)! $

pls i sincerely need ur comment on this, confuse somehow, thank you very much.