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## What are the Bell Numbers?

You come across a reference to a special number sequence, perhaps the Catalan numbers, or the Fibonacci numbers, the Motzkin numbers, the Bell numbers, the lucky numbers, the tetrahedral numbers, the abundant or deficient numbers, etc., and you would like to find out what they are.

Let us take the Bell numbers as an example.

Again you begin by going to the OEIS, where at the foot of the page you see a link to the Index.

You click on the Index, and go to section Be, where you find something like the following.

......

Beethoven: A001491, A054245, A123456
beginning with t: A006092, A005224
Belgian numbers: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043, A107062, A107070.
Bell numbers, sequences related to :

Bell numbers: A000110*

bell ringing , sequences related to

bell ringing: (1) A090277 A090278 A090279 A090280 A090281 A090282 A090283 A090284
bell ringing: (2) A057112 A060112 A060135
......

(The asterisks indicate the most important sequences.)

Clicking on A000110 produces the following reply, which is just what you wanted. The entry gives the beginning of the sequence, a description, references, formulae, Maple and Mathematica programs to generate the sequence, links, cross-references, etc.

This is one of the longest and most interesting entries in the database.

### Greetings from the On-Line Encyclopedia of Integer Sequences!

 A000110 Bell or exponential numbers: ways of placing n labeled balls into n indistinguishable boxes. (Formerly M1484 N0585) 484
 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323, 44152005855084346 (list; graph; refs; listen; history; edit; internal format)