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Recurrence Relations : Stirling Numbers

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A stirling number Snk is defined as the number of ways of partitioning the set of positive numbers (1,2,3......n) into k non empty subsets.

Show Sn,n-2 = (n 3) + 3(n 4) for n>3

The brackets are transposed.

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Recurrence Relations and Stirling Numbers are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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I chall use you notation where you write (n k) = n!/[k!(n-k)!].

There are two kinds of partitions when we partition n numbers into (n-2) subsets:

(A) Partitions in which 3 numbers are in ...

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