Question: Given the sequences a0, a1, a2, . . . and b0, b1,b2, ..., with exponential generating functions f(x), g(x), respectively, show that if h{x) =

Given the sequences a0, a1, a2, . . . and b0, b1,b2, ..., with exponential generating functions f(x), g(x), respectively, show that if h{x) = f(x)g(x), then h{x) is the exponential generating function of the sequence c0, c1, c2, . . ., where cn = ∑ni=o (n1)a1,bn-1 for each n > 0.

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