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Let f(n) be the number of weak ordered 2-partitions (S1, S2) of [n] = {1, 2, ...,n} which satisfies that | S1 2 1 and

Let f(n) be the number of weak ordered 2-partitions (S1, S2) of [n] = {1, 2, ...,n} which satisfies that | S1 2 1 and | S2 |2 2. (a) Show that exponential generating function En "f(n) = = (ex -1)(ex -1 -x). (b) Find a closed formula for f(n)

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