expected(n)=sum(i=1,n,n!/(n-i)!/n^i,0.);
test(n, times)={
  my(ct);
  for(i=1,times,
    my(x=1,bits);
    while(!bitand(bits,x),ct++; bits=bitor(bits,x); x = 1<<random(n))
  );
  ct
};
TIMES=1000000;
{for(n=1,20,
 my(cnt=test(n, TIMES),avg=cnt/TIMES,ex=expected(n),diff=(avg/ex-1)*100.);
 print(n"\t"avg*1."\t"ex*1."\t"diff);
)}