5.56 converting series to factorials

Function by Robert Israel from the net:

restart; 
 
thefacts:= [seq(i!,i=2..20)]: 
  getfacts:= proc(x::{algebraic,series}) 
    local i; 
    if type(x, {`+`,`*`,series}) then 
      map(getfacts,x) 
    elif type(x, fraction) then 
      getfacts(numer(x))/getfacts(denom(x)) 
    elif type(x,`^`) then 
      getfacts(op(1,x))^op(2,x) 
    elif type(x,negint) then 
      -getfacts(-x) 
    elif type(x,posint) then 
      for i from 1 to 19 while irem(x, thefacts[i]) = 0 do od: 
      if i = 1 then x 
      elif thefacts[i-1] = x then ``(i)! 
      else ``(i-1)!*getfacts(x/thefacts[i]) 
      fi 
    else x 
    fi 
  end; 
 
getfacts(series(sin(x),x));
 

\[ \text {series} \left ( x-{\frac {{x}^{3}}{ \left ( \left ( 3 \right ) \right ) !}}+{\frac {{x}^{5}}{ \left ( \left ( 5 \right ) \right ) !}}+O \left ( {x}^{7} \right ) ,x,7 \right ) \]