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Recurrence Relations : Stirling Number

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A Stirling Number Snk is defined as the number of ways of partitioning the set of positive numbers (1,2,3,4....n) into k non empty subsets.

Show S2n,2 = 2n + (2n 2) + (2n 3) + ...... (2n n-1) + 1/2 (2n n)

Everything in brackets is 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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First of all, let me state that the expression given above is not correct. I will give you the correct argument and the solution.

S2n,2 denotes the number of ways the set (1,2,3,4....2n) can be partitioned into 2 non empty subsets.
Say the sets are A and B.
Now the task is to put some elements into A and the rest of the elements into B so that A and B will not ...

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