Quick guide
How to use this calculator
- Enter the number of labeled objects.
- All possible non-empty group counts are included.
- Read the exact Bell number B(n).
Calculation method
Sum the set partitions over every group count
B(n) is the sum of S(n,k) from k=0 through n.
Worked example
Group four labeled objects
Across one, two, three, or four groups, there are fifteen set partitions.
B(4) = 15
Supported inputs
Precision and limits
Discrete domain
Inputs are whole counts. Negative, fractional, grouped, and scientific-notation inputs are rejected.
Exact integers
Results use arbitrary-precision integers and are never rounded. Inputs and output size are bounded to keep the page responsive.
Maximum n
n is limited to 300 for responsive exact evaluation.