n k S dif
0           1           1      1.7183
1           1           2     0.71828
2           2         2.5     0.21828
3           6      2.6667    0.051615
4           24      2.70833    0.0099485
5           120      2.716667   0.001615162
6           720      2.718056  0.0002262729
7           5040       2.718254  2.7860205e-05
8           40320      2.71827877  3.05861778e-06
9           362880      2.718281526  3.028858533e-07
10           3628800      2.7182818011  2.7312661022e-08
11           39916800       2.7182818262  2.26055263397e-09
12           479001600      2.718281828286  1.728768239673e-10
13           6227020800      2.7182818284468  1.2286172079712e-11
14           87178291200      2.71828182845823  8.15347789284715e-13
15          1307674368000      2.718281828458995  5.062616992290714e-14
16         20922789888000      2.718281828459043  2.664535259100376e-15
17        355687428096000      2.718281828459046                      0