$$B(n) = \sum_{k=0}^{n} S(n,k) $$

with the first five Bell numbers :

$\begin{array}{llllll}

&&&&&Total\\

1 &&&&&1 \\

0 & 1 &&&&1\\

0 & 1 & 1 & &&2\\

0 & 1 & 3 & 1 & &5\\

0 & 1 & 7 & 6 & 1&15

\end{array}$

A beautiful recurrence formula for the Bell number is

$$B(n) = \sum_{k=0}^{n-1} B(k) \cdot C(n-1,k) ,$$

for example for n=4 we get: 1* 1+ 1*3 + 2*3 + 5*1 = 15.

I now have the sixth edition of the book Discrete Mathematics and Its Applications by Kenneth Rosen.

A great book which comes with the best accompanying student website I have seen sofar for a mathematics book. It probably takes hours to just to browse through all the applets.

2-2018 Teaching by misleading

2 months ago

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