Bell Number

Problem

Compute the n-th Bell number, the number of ways to partition a set of n items into any number of nonempty blocks.

Use B(n) = sum over k of S(n, k), where S is the Stirling number of the second kind. Return 0 for negative n.

Hint

Sum the Stirling second-kind numbers over all block counts.

case 1

in: [0]

expected: 1

case 2

in: [1]

expected: 1

case 3

in: [3]

expected: 5

case 4

in: [5]

expected: 52

case 5

in: [7]

expected: 877

Starter codePython

import math


def bell_number(n):
    # Your code here
    pass

5 test cases · run your code against them in the editor