Comment l'utiliser (3 étapes)
- 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
Qu’est-ce qu’un nombre de Bell ?
Bell numbers count the total number of partitions of an n-element set.
Quel lien entre les nombres de Bell et les nombres de Stirling ?
Bell numbers satisfy B(n)=Σ S(n,k), the row sum of the second-kind Stirling table.
Puis-je passer aux tableaux de Stirling depuis cette page ?
Yes. Use the type tabs to view S(n,k), s(n,k), or c(n,k) without leaving the page.
Pourquoi utiliser le mode modulo ?
Exact values grow quickly, so modulo arithmetic keeps numbers small for contests and checks.
Pourquoi y a-t-il une limite sur nMax ?
Exact values are enormous and large tables are costly to render, so the calculator clamps nMax for stability.
Puis-je exporter le tableau ?
Yes. Use the CSV or TSV export buttons to download the full table.