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

Question

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

Kunduz · Accepted Answer

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