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September 21, 2006
What's next ? 1, 1, 2, 5, 15, 52, 203, ???
If you recognized the first few Bell numbers, you would, of course, have guessed 877 immediately. Otherwise, you would have done like me and headed off to the fantastic On-Line Encyclopedia of Integer Sequences I've just recently discovered. A quick query for:
http://www.research.att.com/~njas/sequences/?q=1+1+2+5+15+52+203
Would take you straight to sequence A00110, also known as "Bell or exponential numbers: ways of placing n labeled balls into n indistinguishable boxes. It can also be expressed as this short formula (among others):
a(n) = exp(-1)*sum(k=>0, k^n/k!)
I love this, as I've always loved/hated these types of puzzles. And it has many more usefull uses, as is pointed out by their demo.
Posted by gozer at September 21, 2006 12:35 AM