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 It's e-asy (Posted on 2008-02-19)
Outline a method for calculating Sk = Σ nk/n! for n=1 to infinity and compute the first few terms of Sk for natural numbers k.

 See The Solution Submitted by FrankM Rating: 2.0000 (2 votes)

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 re: computer solution | Comment 2 of 7 |
(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

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