Outline a method for calculating S_k = Σ n^k/n! for n=1 to infinity and compute the first few terms of S_k for natural numbers k.

(In reply to computer solution by Charlie)

Using greater precision UBASIC, we can extend the Bell numbers beyond what shows in Sloan:

list
   10   point 18
   20   for K=1 to 25
   30   T=0
   40   Term=1:F=1
   50   for N=1 to 44
   60     F=F*N
   70     Term=N^K/F
   80     T=T+Term
   90   next
  100   print K;int(T/exp(1)+0.5)
  110   next
OK

run
 1  1
 2  2
 3  5
 4  15
 5  52
 6  203
 7  877
 8  4140
 9  21147
 10  115975
 11  678570
 12  4213597
 13  27644437
 14  190899322
 15  1382958545
 16  10480142147
 17  82864869804
 18  682076806159
 19  5832742205057
 20  51724158235372
 21  474869816156751
 22  4506715738447323
 23  44152005855084346
 24  445958869294805289
 25  4638590332229999353
OK

Posted by Charlie on 2008-02-19 13:03:43