Stirling numbers of the second kind
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This page is a solution to the task Stirling numbers of the second kind in the Rosetta Code, written in Fōrmulæ.
Description (from Rosetta Code)
Stirling numbers of the second kind, or Stirling partition numbers, are the number of ways to partition a set of n objects into k nonempty subsets. They are closely related to Bell numbers, and may be derived from them.
Stirling numbers of the second kind obey the recurrence relation: S2(n, 0) and S2(0, k) = 0 # for n, k > 0 S2(n, n) = 1 S2(n + 1, k) = k * S2(n, k) + S2(n, k  1)

Solution
Recursive
Table up to S2(12, 12):
Non recursive
A faster, non recursive version is presented:
Table up to S2(12, 12):
(The result is the same as recursive version)
Extra
Maximum value of S2(100, k) for k ≤ 100: