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Prove that the Stirling numbers of the second kind satisfy the following relations:
1) S(n,1)=1 when n>=1
2) S(n,2)=2^(n-1)-1 when n>=2
3) S(n, n-1) = (n choose 2) when n>=1
4) S(n, n-2) = (n choose 3) + 3(n choose 4) when n>=2
[note:
S(n,p) means the number of ways to partition n elements into p subsets.
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