### Related

belln(1001);

Calculate

belln(1001);

Calculate

##### belln

belln(100)/(1000*3600...

Calculate

##### belln

belln(100)/(1000*3600...

Calculate

? belln;

Calculate

##### belln

belln(100)/(1000*3600...

Calculate

##### belln

belln(100)/(1000*3600...

Calculate

##### belln-cardinality-makelist-set_partitions-sqrt

makelist (belln (i), ...

is (cardinality (set...

is (cardinality (set...

Calculate

##### belln-cardinality-makelist-set_partitions-sqrt

makelist (belln (i), ...

is (cardinality (set...

is (cardinality (set...

Calculate

? belln;

Calculate

### belln

Run Example
```(%i1)belln(100);
(%o1) 475853912767648336587907688413872078263636696868256114666163346375591144\
97892442622672724044217756306953557882560751
(%i2) ```
Run Example
```belln(1001);
(%o1) 569749244411564056701989455110467044188729937775050781483244428792654813\
571847398922658885461975327751098927411167692969232643128761842731042958270297\
794303854701785335516979467700999949950986168189932196873193021013564990178545\
758876640477512693712561126347259131354918843802623603359187229834868564321824\
824107098766099742590741828838727514784526390233989646601835970452424519501674\
589775478038230020329456222837789669276373295818434377503974832769841542402530\
875682374242014888243356295302710283786791147763903758520836668531417219553769\
023895924230681715093855618583233585599501575933488517493084470545299107701096\
882635149726969085858631028615714715440195193903384982324261700731822242872454\
995494307216900407277154362237446389720953333006176489562964912303609050913741\
203851762863116528532658455577020502151224600231687724141817499110157512534328\
176335717474374810153100585990924101147414511294970741920955935961662738094859\
636443890778912658364283446296754332671555913356907624223607865103886033168781\
141207383985515428684980891264237930108487260524991359869150067508471413446409\
555768953478870300398039111686227524700988777518986030152935560770428910702791\
693446974884722781150456314197578708251947599682946382578946411942765161244371\
490848800496758370064859772498943785903240308478764495206997313304890944550434\
076918198970595539145850117678543127418915477679608300053693170507173717326646\
306805564351381812884576495939590276669954656243951805248196432425869325824311\
174917564151966834519709588380309990558101944385177462347634920975040651132936\
610285787564740574675646430232267661828135663782462244856851626868422983998265\
033144248107741372289006094400240934653027321295337196644611798809781514038338\
665832985472243517647656875933151575039897303032562091530879379710327550874408\
419507785965007258475672052588620611388261078061140065572854899786461175808547\
0239474795626811763535347752489904986818946011595325092664416060
(%i2) ```
Run Example
```? belln;

-- Function: belln (<n>)
Represents the n-th Bell number.  `belln(n)' is the number of
partitions of a set with <n> members.

For nonnegative integers <n>, `belln(<n>)' simplifies to the n-th
Bell number.  `belln' does not simplify for any other arguments.

`belln' distributes over equations, lists, matrices, and sets.

Examples:

`belln' applied to nonnegative integers.

(%i1) makelist (belln (i), i, 0, 6);
(%o1)               [1, 1, 2, 5, 15, 52, 203]
(%i2) is (cardinality (set_partitions ({})) = belln (0));
(%o2)                         true
(%i3) is (cardinality (set_partitions ({1, 2, 3, 4, 5, 6})) =
belln (6));
(%o3)                         true

`belln' applied to arguments which are not nonnegative integers.

(%i1) [belln (x), belln (sqrt(3)), belln (-9)];
(%o1)        [belln(x), belln(sqrt(3)), belln(- 9)]

(%o1)                                true
(%i2) ```

Help for Belln