Stirling Number Calculator

Calculate Stirling numbers of the first and second kind.

Parameters

n (elements)

k (subsets)

S(5, 3)

25

Number of ways to partition 5 elements into 3 non-empty subsets

Stirling Triangle (Second Kind)

n\k012345

0

1

1

0

1

2

0

1

1

3

0

1

3

1

4

0

1

7

6

1

5

0

1

15

25

10

1

Row Sums

Row 0

1

Row 1

1

Row 2

2

Row 3

5

Row 4

15

Row 5

52

Recurrence Relations

Second Kind

S(n,k) = k×S(n-1,k) + S(n-1,k-1)

First Kind

|s(n,k)| = (n-1)×|s(n-1,k)| + |s(n-1,k-1)|