How this calculation works
Count all partitions of a labeled set, allowing any number of nonempty groups.
THE FORMULA
Bₙ₊₁=Σ C(n,k)BₖA worked example
Five elements give 52 partitions.
Good to know
Groups have no order.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Count all partitions of a labeled set, allowing any number of nonempty groups.
The primary result is labeled “Partitions”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Groups have no order.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
Five elements give 52 partitions.
Which rule does this calculator apply?
Bₙ₊₁=Σ C(n,k)Bₖ