How to use (3 steps)
- Keep Bell selected or switch to a Stirling type tab.
- Set nMax and choose Exact or Mod mode.
- Tap a row to read the meaning, then export or share.
Bell numbers and Stirling links
- Bell numbers count all set partitions: B(n)=Σ S(n,k).
- The second-kind Stirling table gives the row-wise breakdown by block count.
- Use the first-kind tabs to switch to cycle-count tables for permutations.
- Recurrence: B(n+1)=Σ C(n,k)B(k).
Example values
- B(5)=52.
- B(6)=203.
- B(8)=4140.
FAQ
What is a Bell number?
Bell numbers count the total number of partitions of an n-element set.
How are Bell numbers related to Stirling numbers?
Bell numbers satisfy B(n)=Σ S(n,k), the row sum of the second-kind Stirling table.
Can I switch to Stirling tables from this page?
Yes. Use the type tabs to view S(n,k), s(n,k), or c(n,k) without leaving the page.
Why use modulo mode?
Exact values grow quickly, so modulo arithmetic keeps numbers small for contests and checks.
Why is there a limit on nMax?
Exact values are enormous and large tables are costly to render, so the calculator clamps nMax for stability.
Can I export the table?
Yes. Use the CSV or TSV export buttons to download the full table.