Stirling numbers of the second kind
This online calculator outputs Stirling numbers of the second kind for the given n
In combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k nonempty subsets and is denoted by S(n,k)^{1}. This online calculator calculates the Stirling number of the second kind for the given n, for each k from 0 to n and outputs results into a table. Note that this calculator uses the "big integers" library (see Tips and tricks #9: Big numbers), so you can try pretty big n values.
For example, the number of ways to partition a set of 100 objects into 28 nonempty subsets is 77697 3005359874 5155212806 6127875847 8739787812 8370115840 9749925701 0238608628 9805848025 0748224048 4354517896 0761551674. A combinatorial explosion, that is :)
For those who curious, the explicit formula is listed below the calculator.
Stirling numbers formula

Ronald L. Graham, Donald E. Knuth, Oren Patashnik (1988) Concrete Mathematics, Addison–Wesley, Reading MA. ISBN 0201142368, p. 244. ↩
Similar calculators
 • Combinatorics. Permutation generator from N to M with repetitions.
 • Stirling's approximation of factorial
 • Combinatorics. Permutation generator from n to m without repetitions
 • Combinatorics – combinations, arrangements and permutations
 • Making up words out of the syllables
 • Combinatorics section ( 29 calculators )
Comments