n=6 reps=4000000 seed=5 imax=30  partial sum_{i<=imax} i*EN_i=30.00 (full=30)
A 2 0.833304062500
A 3 0.728785625000
A 4 0.624922929687
A 5 0.535840498047
A 6 0.456954482422
A 7 0.382135834961
A 8 0.320698784180
A 9 0.261671381836
A 10 0.214614628906
A 11 0.168995786133
A 12 0.134619819336
A 13 0.102379750977
A 14 0.077557158203
A 15 0.055540307617
A 16 0.039909086914
A 17 0.026030991211
A 18 0.017017583008
A 19 0.009638320313
A 20 0.005594843750
A 21 0.001935625000
A 22 0.001852500000
A 23 0.000000000000
A 24 0.000000000000
A 25 0.000000000000
A 26 0.000000000000
A 27 0.000000000000
A 28 0.000000000000
A 29 0.000000000000
A 30 0.000000000000
y=0.25  i=4  r=E N_i e^{i/n}=1.21718 +- 0.00044   e^{-i^2/(2n^3)}=0.96364  ratio_to_thm1=1.26311
y=0.50  i=7  r=E N_i e^{i/n}=1.22714 +- 0.00051   e^{-i^2/(2n^3)}=0.89277  ratio_to_thm1=1.37453
y=1.00  i=15  r=E N_i e^{i/n}=0.67662 +- 0.00083   e^{-i^2/(2n^3)}=0.59403  ratio_to_thm1=1.13904
y=1.50  i=22  r=E N_i e^{i/n}=0.07247 +- 0.00188   e^{-i^2/(2n^3)}=0.32616  ratio_to_thm1=0.22220
y=2.00  i=29  r=E N_i e^{i/n}=0.00000 +- 0.00000   e^{-i^2/(2n^3)}=0.14274  ratio_to_thm1=0.00000
x=1     i=6  r=E N_i e^{i/n}=1.24213 +- 0.00048   e^{-i^2/(2n^3)}=0.92004  ratio_to_thm1=1.35008
x=2     i=12  r=E N_i e^{i/n}=0.99471 +- 0.00071   e^{-i^2/(2n^3)}=0.71653  ratio_to_thm1=1.38823
x=4     i=24  r=E N_i e^{i/n}=0.00000 +- 0.00000   e^{-i^2/(2n^3)}=0.26360  ratio_to_thm1=0.00000
