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The Maxima on-line user's manual

Algebra Calculator

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Belln Calculator

Belln

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

makelist (belln (i), i, 0, 6);
 is (cardinality (set_partitions ({})) = belln (0));
 is (cardinality (set_partitions ({1, 2, 3, 4, 5, 6})) =                                 belln (6));
 [belln (x), belln (sqrt(3)), belln (-9)];

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) 

Belln Example

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