Bell Number

Note 1 : Write a Program in any Language

Note 2 : If you have any doubt ask in comment

Note 3 : Read problem carefuly.

The Bell number is the number of ways an array of n items can be partitioned into non-empty subarrays.

In general, Bn is the number of partitions of a set of size n. A partition of a set S is defined as a set of nonempty, pairwise disjoint subsets of S whose union is S. For example, B3 = 5 because the 3-element set {a, b, c} can be partitioned in 5 distinct ways:

{ {a}, {b}, {c} }
{ {a}, {b, c} }
{ {b}, {a, c} }
{ {c}, {a, b} }
{ {a, b, c} }

Create a function that takes a number n and returns the corresponding Bell number.

Example:

bell(1) ➞ 1
// sampleArr = [1]
// possiblePartitions = [[[1]]]

bell(2) ➞ 2
// sampleArr = [1, 2]
// possiblePartitions = [[[1, 2]], [[1], [2]]]

bell(3) ➞ 5
// sampleArr = [1, 2, 3]
// possiblePartitions = [[[1, 2, 3]], [[1, 2], [3]], [[1], [2, 3]], [[1, 3], [2]], [[1], [2], [3]]]

Coding Challenge for U 12 - Bell Number