### The Maxima on-line user's manual

Algebra Calculator

#### 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)

### Related Examples

belln(100);

Calculate

belln(1001);

Calculate

belln(100);

Calculate

? belln;

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? belln;

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##### 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

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

Calculate

belln(1001);

Calculate