const N=20;

(" N    average    analytical    (error)").println();
("===  =========  ============  =========").println();
foreach n in ([1..N]){
   a := avg(n);
   b := ana(n);
   "%3d  %9.4f  %12.4f  (%6.2f%%)".fmt(
            n, a, b, ((a-b)/b*100)).println();
}

fcn f(n){ (0).random(n) }

fcn avg(n){
   tests := 0d10_000;
   sum := 0;
   do(tests){
      v:=(0).pump(n,List,T(Void,False)).copy();
      while(1){
         z := f(n);
         if(v[z]) break;
	 v[z] = True;
	 sum += 1;
      }
   }
   return(sum.toFloat() / tests);
}

fcn fact(n) { (1).reduce(n,fcn(N,n){N*n},1.0) } //-->Float
fcn ana(n){
   n=n.toFloat();
   (1).reduce(n,'wrap(sum,i){ sum+fact(n)/n.pow(i)/fact(n-i) },0.0);
}